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id="page-actions-watch" class="page-actions-menu__list-item"> <a role="button" id="ca-watch" href="/w/index.php?title=Special:UserLogin&returnto=F-number" data-event-name="menu.watch" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet menu__item--page-actions-watch"> Watch </a> </li> <li id="page-actions-edit" class="page-actions-menu__list-item"> <a role="button" id="ca-edit" href="/w/index.php?title=F-number&action=edit" data-event-name="menu.edit" data-mw="interface" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet edit-page menu__item--page-actions-edit"> Edit </a> </li> </ul> </nav>  <div id="mw-content-subtitle"></div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"><script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><section class="mf-section-0" id="mf-section-0"> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/F-number_(disambiguation)" class="mw-disambig" title="F-number (disambiguation)">F-number (disambiguation)</a>.</div> An f-number is a measure of the light-gathering ability of an optical system such as a <a href="/wiki/Camera_lens" title="Camera lens">camera lens</a>. It is calculated by dividing the system's <a href="/wiki/Focal_length" title="Focal length">focal length</a> by the diameter of the <a href="/wiki/Entrance_pupil" title="Entrance pupil">entrance pupil</a> ("clear <a href="/wiki/Aperture" title="Aperture">aperture</a>").<a href="#cite_note-ReferenceA-1">[1]</a><a href="#cite_note-2">[2]</a><a href="#cite_note-3">[3]</a> The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the <a href="/wiki/Depth_of_field" title="Depth of field">depth of field</a>, <a href="/wiki/Diffraction" title="Diffraction">diffraction</a>, and <a href="/wiki/Exposure_(photography)" title="Exposure (photography)">exposure</a> of a photograph.<a href="#cite_note-4">[4]</a> The f-number is <a href="/wiki/Dimensionless_number" class="mw-redirect" title="Dimensionless number">dimensionless</a> and is usually expressed using a lower-case <a href="/wiki/%C6%91" title="Ƒ">hooked f</a> with the format <style data-mw-deduplicate="TemplateStyles:r1207775266">.mw-parser-output span.fnumber,.mw-parser-output .fnumber-fallback{display:inline-block;white-space:nowrap;width:max-content}.mw-parser-output span.fnumber::first-letter,.mw-parser-output .fnumber-fallback .first-letter{font-style:italic;font-family:Trebuchet MS,Candara,Georgia,Calibri,Corbel,serif}</style>f/N, where N is the f-number. <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Aperture_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Aperture_diagram.svg/320px-Aperture_diagram.svg.png" decoding="async" width="320" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Aperture_diagram.svg/480px-Aperture_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Aperture_diagram.svg/640px-Aperture_diagram.svg.png 2x" data-file-width="512" data-file-height="204"></a><figcaption>Diagram of decreasing <a href="/wiki/Aperture" title="Aperture">apertures</a>, that is, increasing f-numbers, in one-stop increments; each aperture has half the light-gathering area of the previous one.</figcaption></figure> The f-number is also known as the inverse relative aperture, because it is the <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">inverse</a> of the relative aperture, defined as the aperture diameter divided by focal length.<a href="#cite_note-5">[5]</a> The relative aperture indicates how much light can pass through the lens at a given focal length. A lower f-number means a larger relative aperture and more light entering the system, while a higher f-number means a smaller relative aperture and less light entering the system. The f-number is related to the <a href="/wiki/Numerical_aperture" title="Numerical aperture">numerical aperture</a> (NA) of the system, which measures the range of angles over which light can enter or exit the system. The numerical aperture takes into account the <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> of the medium in which the system is working, while the f-number does not. <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><label class="toctogglelabel" for="toctogglecheckbox"></label></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Notation">1 Notation</a></li> <li class="toclevel-1 tocsection-2"><a href="#Stops,_f-stop_conventions,_and_exposure">2 Stops, f-stop conventions, and exposure</a> <ul> <li class="toclevel-2 tocsection-3"><a href="#Fractional_stops">2.1 Fractional stops</a> <ul> <li class="toclevel-3 tocsection-4"><a href="#Standard_full-stop_f-number_scale">2.1.1 Standard full-stop f-number scale</a></li> <li class="toclevel-3 tocsection-5"><a href="#Typical_one-half-stop_f-number_scale">2.1.2 Typical one-half-stop f-number scale</a></li> <li class="toclevel-3 tocsection-6"><a href="#Typical_one-third-stop_f-number_scale">2.1.3 Typical one-third-stop f-number scale</a></li> <li class="toclevel-3 tocsection-7"><a href="#Typical_one-quarter-stop_f-number_scale">2.1.4 Typical one-quarter-stop f-number scale</a></li> </ul> </li> <li class="toclevel-2 tocsection-8"><a href="#H-stop">2.2 H-stop</a></li> <li class="toclevel-2 tocsection-9"><a href="#T-stop">2.3 T-stop</a></li> <li class="toclevel-2 tocsection-10"><a href="#ASA/ISO_numbers">2.4 ASA/ISO numbers</a></li> <li class="toclevel-2 tocsection-11"><a href="#Gain">2.5 Gain</a></li> <li class="toclevel-2 tocsection-12"><a href="#Sunny_16_rule">2.6 Sunny 16 rule</a></li> </ul> </li> <li class="toclevel-1 tocsection-13"><a href="#Effects_on_image_sharpness">3 Effects on image sharpness</a></li> <li class="toclevel-1 tocsection-14"><a href="#Human_eye">4 Human eye</a></li> <li class="toclevel-1 tocsection-15"><a href="#Focal_ratio_in_telescopes">5 Focal ratio in telescopes</a></li> <li class="toclevel-1 tocsection-16"><a href="#Camera_equation_(G#)">6 Camera equation (G#)</a></li> <li class="toclevel-1 tocsection-17"><a href="#Working_f-number">7 Working f-number</a></li> <li class="toclevel-1 tocsection-18"><a href="#History">8 History</a> <ul> <li class="toclevel-2 tocsection-19"><a href="#Origins_of_relative_aperture">8.1 Origins of relative aperture</a></li> <li class="toclevel-2 tocsection-20"><a href="#Aperture_numbering_systems">8.2 Aperture numbering systems</a></li> <li class="toclevel-2 tocsection-21"><a href="#Typographical_standardization">8.3 Typographical standardization</a></li> </ul> </li> <li class="toclevel-1 tocsection-22"><a href="#See_also">9 See also</a></li> <li class="toclevel-1 tocsection-23"><a href="#References">10 References</a></li> <li class="toclevel-1 tocsection-24"><a href="#External_links">11 External links</a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><h2 id="Notation">Notation</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=1" title="Edit section: Notation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> The f-number N is given by: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N={\frac {f}{D}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <mi>D</mi> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N={\frac {f}{D}}\ }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f77eef5650185f41f729e3b0c6fd1fc1aea1f22" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.503ex; height:5.343ex;" alt="{\displaystyle N={\frac {f}{D}}\ }"></noscript><span class="lazy-image-placeholder" style="width: 8.503ex;height: 5.343ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f77eef5650185f41f729e3b0c6fd1fc1aea1f22" data-alt="{\displaystyle N={\frac {f}{D}}\ }" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  where f is the <a href="/wiki/Focal_length" title="Focal length">focal length</a>, and D is the diameter of the entrance pupil (effective aperture). It is customary to write f-numbers preceded by "<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/", which forms a mathematical expression of the entrance pupil's diameter in terms of f and N.<a href="#cite_note-ReferenceA-1">[1]</a> For example, if a <a href="/wiki/Lens_(optics)" class="mw-redirect" title="Lens (optics)">lens's</a> focal length were 100 mm and its entrance pupil's diameter were 50 mm, the f-number would be 2. This would be expressed as "<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2" in a lens system. The aperture diameter would be equal to f/2. Camera lenses often include an adjustable <a href="/wiki/Diaphragm_(optics)" title="Diaphragm (optics)">diaphragm</a>, which changes the size of the <a href="/wiki/Aperture_stop" class="mw-redirect" title="Aperture stop">aperture stop</a> and thus the entrance pupil size. This allows the user to vary the f-number as needed. The entrance pupil diameter is not necessarily equal to the aperture stop diameter, because of the magnifying effect of lens elements in front of the aperture. Ignoring differences in light transmission efficiency, a lens with a greater f-number projects darker images. The brightness of the projected image (<a href="/wiki/Illuminance" title="Illuminance">illuminance</a>) relative to the brightness of the scene in the lens's field of view (<a href="/wiki/Luminance" title="Luminance">luminance</a>) decreases with the square of the f-number. A 100 mm focal length <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/4 lens has an entrance pupil diameter of 25 mm. A 100 mm focal length <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2 lens has an entrance pupil diameter of 50 mm. Since the area is proportional to the square of the pupil diameter,<a href="#cite_note-6">[6]</a> the amount of light admitted by the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2 lens is four times that of the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/4 lens. To obtain the same <a href="/wiki/Exposure_(photography)" title="Exposure (photography)">photographic exposure</a>, the exposure time must be reduced by a factor of four. A 200 mm focal length <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/4 lens has an entrance pupil diameter of 50 mm. The 200 mm lens's entrance pupil has four times the area of the 100 mm <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/4 lens's entrance pupil, and thus collects four times as much light from each object in the lens's field of view. But compared to the 100 mm lens, the 200 mm lens projects an image of each object twice as high and twice as wide, covering four times the area, and so both lenses produce the same illuminance at the focal plane when imaging a scene of a given luminance. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><h2 id="Stops,_f-stop_conventions,_and_exposure">Stops, f-stop conventions, and exposure</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=2" title="Edit section: Stops, f-stop conventions, and exposure" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Canon_7_with_50mm_f0.95_IMG_0374.JPG" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Canon_7_with_50mm_f0.95_IMG_0374.JPG/220px-Canon_7_with_50mm_f0.95_IMG_0374.JPG" decoding="async" width="220" height="220" class="mw-file-element" data-file-width="2730" data-file-height="2736"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 220px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Canon_7_with_50mm_f0.95_IMG_0374.JPG/220px-Canon_7_with_50mm_f0.95_IMG_0374.JPG" data-width="220" data-height="220" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Canon_7_with_50mm_f0.95_IMG_0374.JPG/330px-Canon_7_with_50mm_f0.95_IMG_0374.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Canon_7_with_50mm_f0.95_IMG_0374.JPG/440px-Canon_7_with_50mm_f0.95_IMG_0374.JPG 2x" data-class="mw-file-element"> </a><figcaption>A <a href="/wiki/Canon_7" title="Canon 7">Canon 7</a> mounted with a 50 mm lens capable of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/0.95</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Lens_aperture_side.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Lens_aperture_side.jpg/220px-Lens_aperture_side.jpg" decoding="async" width="220" height="220" class="mw-file-element" data-file-width="1200" data-file-height="1200"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 220px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Lens_aperture_side.jpg/220px-Lens_aperture_side.jpg" data-width="220" data-height="220" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Lens_aperture_side.jpg/330px-Lens_aperture_side.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Lens_aperture_side.jpg/440px-Lens_aperture_side.jpg 2x" data-class="mw-file-element"> </a><figcaption>A 35 mm lens set to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/11, as indicated by the white dot above the f-stop scale on the aperture ring. This lens has an aperture range of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2 to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/22.</figcaption></figure> The word stop is sometimes confusing due to its multiple meanings. A stop can be a physical object: an opaque part of an optical system that blocks certain rays. The <a href="/wiki/Aperture_stop" class="mw-redirect" title="Aperture stop">aperture stop</a> is the aperture setting that limits the brightness of the image by restricting the input pupil size, while a field stop is a stop intended to cut out light that would be outside the desired field of view and might cause flare or other problems if not stopped. In photography, stops are also a unit used to quantify ratios of light or exposure, with each added stop meaning a factor of two, and each subtracted stop meaning a factor of one-half. The one-stop unit is also known as the EV (<a href="/wiki/Exposure_value" title="Exposure value">exposure value</a>) unit. On a camera, the aperture setting is traditionally adjusted in discrete steps, known as f-stops. Each "stop" is marked with its corresponding f-number, and represents a halving of the light intensity from the previous stop. This corresponds to a decrease of the pupil and aperture diameters by a factor of 1/√2 or about 0.7071, and hence a halving of the area of the pupil. Most modern lenses use a standard f-stop scale, which is an approximately <a href="/wiki/Geometric_sequence" class="mw-redirect" title="Geometric sequence">geometric sequence</a> of numbers that corresponds to the sequence of the <a href="/wiki/Exponentiation" title="Exponentiation">powers</a> of the <a href="/wiki/Square_root_of_2" title="Square root of 2">square root of 2</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/1, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/1.4, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2.8, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/4, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/5.6, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/11, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/16, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/22, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/32, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/45, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/64, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/90, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/128, etc. Each element in the sequence is one stop lower than the element to its left, and one stop higher than the element to its right. The values of the ratios are rounded off to these particular conventional numbers, to make them easier to remember and write down. The sequence above is obtained by approximating the following exact geometric sequence: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f/1={\frac {f}{({\sqrt {2}})^{0}}},\ f/1.4={\frac {f}{({\sqrt {2}})^{1}}},\ f/2={\frac {f}{({\sqrt {2}})^{2}}},\ f/2.8={\frac {f}{({\sqrt {2}})^{3}}},\ \ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>1</mn> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>1.4</mn> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2.8</mn> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f/1={\frac {f}{({\sqrt {2}})^{0}}},\ f/1.4={\frac {f}{({\sqrt {2}})^{1}}},\ f/2={\frac {f}{({\sqrt {2}})^{2}}},\ f/2.8={\frac {f}{({\sqrt {2}})^{3}}},\ \ldots }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc386280321ff746234d3fbe04ddc3b6f1ee18ac" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:67.187ex; height:6.509ex;" alt="{\displaystyle f/1={\frac {f}{({\sqrt {2}})^{0}}},\ f/1.4={\frac {f}{({\sqrt {2}})^{1}}},\ f/2={\frac {f}{({\sqrt {2}})^{2}}},\ f/2.8={\frac {f}{({\sqrt {2}})^{3}}},\ \ldots }"></noscript><span class="lazy-image-placeholder" style="width: 67.187ex;height: 6.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc386280321ff746234d3fbe04ddc3b6f1ee18ac" data-alt="{\displaystyle f/1={\frac {f}{({\sqrt {2}})^{0}}},\ f/1.4={\frac {f}{({\sqrt {2}})^{1}}},\ f/2={\frac {f}{({\sqrt {2}})^{2}}},\ f/2.8={\frac {f}{({\sqrt {2}})^{3}}},\ \ldots }" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  In the same way as one f-stop corresponds to a factor of two in light intensity, <a href="/wiki/Shutter_speed" title="Shutter speed">shutter speeds</a> are arranged so that each setting differs in duration by a factor of approximately two from its neighbour. Opening up a lens by one stop allows twice as much light to fall on the film in a given period of time. Therefore, to have the same exposure at this larger aperture as at the previous aperture, the shutter would be opened for half as long (i.e., twice the speed). The film will respond equally to these equal amounts of light, since it has the property of <a href="/wiki/Reciprocity_(photography)" title="Reciprocity (photography)">reciprocity</a>. This is less true for extremely long or short exposures, where there is <a href="/wiki/Reciprocity_failure" class="mw-redirect" title="Reciprocity failure">reciprocity failure</a>. Aperture, shutter speed, and film sensitivity are linked: for constant scene brightness, doubling the aperture area (one stop), halving the shutter speed (doubling the time open), or using a film twice as sensitive, has the same effect on the exposed image. For all practical purposes extreme accuracy is not required (mechanical shutter speeds were notoriously inaccurate as wear and lubrication varied, with no effect on exposure). It is not significant that aperture areas and shutter speeds do not vary by a factor of precisely two. Photographers sometimes express other <a href="/wiki/Exposure_(photography)" title="Exposure (photography)">exposure</a> ratios in terms of 'stops'. Ignoring the f-number markings, the f-stops make a <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic scale</a> of exposure intensity. Given this interpretation, one can then think of taking a half-step along this scale, to make an exposure difference of a "half stop". <div class="mw-heading mw-heading3"><h3 id="Fractional_stops">Fractional stops</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=3" title="Edit section: Fractional stops" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:248px;max-width:248px"><div class="trow"><div class="tsingle" style="width:122px;max-width:122px"><div class="thumbimage"><a href="/wiki/File:Povray_focal_blur_animation.gif" class="mw-file-description"><noscript><img alt="Changing a camera's aperture in half-stops" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Povray_focal_blur_animation.gif/120px-Povray_focal_blur_animation.gif" decoding="async" width="120" height="90" class="mw-file-element" data-file-width="512" data-file-height="384"></noscript><span class="lazy-image-placeholder" style="width: 120px;height: 90px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Povray_focal_blur_animation.gif/120px-Povray_focal_blur_animation.gif" data-alt="Changing a camera's aperture in half-stops" data-width="120" data-height="90" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Povray_focal_blur_animation.gif/180px-Povray_focal_blur_animation.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Povray_focal_blur_animation.gif/240px-Povray_focal_blur_animation.gif 2x" data-class="mw-file-element"> </a></div></div><div class="tsingle" style="width:122px;max-width:122px"><div class="thumbimage"><a href="/wiki/File:Povray_focal_blur_animation_mode_tan.gif" class="mw-file-description"><noscript><img alt="Changing a camera's aperture from zero to infinity" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Povray_focal_blur_animation_mode_tan.gif/120px-Povray_focal_blur_animation_mode_tan.gif" decoding="async" width="120" height="90" class="mw-file-element" data-file-width="512" data-file-height="384"></noscript><span class="lazy-image-placeholder" style="width: 120px;height: 90px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Povray_focal_blur_animation_mode_tan.gif/120px-Povray_focal_blur_animation_mode_tan.gif" data-alt="Changing a camera's aperture from zero to infinity" data-width="120" data-height="90" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Povray_focal_blur_animation_mode_tan.gif/180px-Povray_focal_blur_animation_mode_tan.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Povray_focal_blur_animation_mode_tan.gif/240px-Povray_focal_blur_animation_mode_tan.gif 2x" data-class="mw-file-element"> </a></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">Computer simulation showing the effects of changing a camera's aperture in half-stops (at left) and from zero to infinity (at right)</div></div></div></div> Most twentieth-century cameras had a continuously variable aperture, using an <a href="/wiki/Iris_diaphragm" class="mw-redirect" title="Iris diaphragm">iris diaphragm</a>, with each full stop marked. Click-stopped aperture came into common use in the 1960s; the aperture scale usually had a click stop at every whole and half stop. On modern cameras, especially when aperture is set on the camera body, f-number is often divided more finely than steps of one stop. Steps of one-third stop (<style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>1⁄3 EV) are the most common, since this matches the ISO system of <a href="/wiki/Film_speed" title="Film speed">film speeds</a>. Half-stop steps are used on some cameras. Usually the full stops are marked, and the intermediate positions click but are not marked. As an example, the aperture that is one-third stop smaller than <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2.8 is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/3.2, two-thirds smaller is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/3.5, and one whole stop smaller is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/4. The next few f-stops in this sequence are: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f/4.5,\ f/5,\ f/5.6,\ f/6.3,\ f/7.1,\ f/8,\ \ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4.5</mn> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>5</mn> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>5.6</mn> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>6.3</mn> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>7.1</mn> <mo>,</mo> <mtext> </mtext> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>8</mn> <mo>,</mo> <mtext> </mtext> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f/4.5,\ f/5,\ f/5.6,\ f/6.3,\ f/7.1,\ f/8,\ \ldots }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/097247d5e2fe6d13a82a927cbbd8b75c126cf14f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.656ex; height:2.843ex;" alt="{\displaystyle f/4.5,\ f/5,\ f/5.6,\ f/6.3,\ f/7.1,\ f/8,\ \ldots }"></noscript><span class="lazy-image-placeholder" style="width: 41.656ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/097247d5e2fe6d13a82a927cbbd8b75c126cf14f" data-alt="{\displaystyle f/4.5,\ f/5,\ f/5.6,\ f/6.3,\ f/7.1,\ f/8,\ \ldots }" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  To calculate the steps in a full stop (1 EV) one could use <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\sqrt {2}})^{0},\ ({\sqrt {2}})^{1},\ ({\sqrt {2}})^{2},\ ({\sqrt {2}})^{3},\ ({\sqrt {2}})^{4},\ \ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\sqrt {2}})^{0},\ ({\sqrt {2}})^{1},\ ({\sqrt {2}})^{2},\ ({\sqrt {2}})^{3},\ ({\sqrt {2}})^{4},\ \ldots }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebb1ba80d09347b1a7b33a9b56940b20804a3eb7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.993ex; height:3.176ex;" alt="{\displaystyle ({\sqrt {2}})^{0},\ ({\sqrt {2}})^{1},\ ({\sqrt {2}})^{2},\ ({\sqrt {2}})^{3},\ ({\sqrt {2}})^{4},\ \ldots }"></noscript><span class="lazy-image-placeholder" style="width: 40.993ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebb1ba80d09347b1a7b33a9b56940b20804a3eb7" data-alt="{\displaystyle ({\sqrt {2}})^{0},\ ({\sqrt {2}})^{1},\ ({\sqrt {2}})^{2},\ ({\sqrt {2}})^{3},\ ({\sqrt {2}})^{4},\ \ldots }" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  The steps in a half stop (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄2 EV) series would be <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\sqrt {2}})^{\frac {0}{2}},\ ({\sqrt {2}})^{\frac {1}{2}},\ ({\sqrt {2}})^{\frac {2}{2}},\ ({\sqrt {2}})^{\frac {3}{2}},\ ({\sqrt {2}})^{\frac {4}{2}},\ \ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\sqrt {2}})^{\frac {0}{2}},\ ({\sqrt {2}})^{\frac {1}{2}},\ ({\sqrt {2}})^{\frac {2}{2}},\ ({\sqrt {2}})^{\frac {3}{2}},\ ({\sqrt {2}})^{\frac {4}{2}},\ \ldots }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce538bd3a2e636348599d46b45fb53b43d315515" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.4ex; height:4.009ex;" alt="{\displaystyle ({\sqrt {2}})^{\frac {0}{2}},\ ({\sqrt {2}})^{\frac {1}{2}},\ ({\sqrt {2}})^{\frac {2}{2}},\ ({\sqrt {2}})^{\frac {3}{2}},\ ({\sqrt {2}})^{\frac {4}{2}},\ \ldots }"></noscript><span class="lazy-image-placeholder" style="width: 44.4ex;height: 4.009ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce538bd3a2e636348599d46b45fb53b43d315515" data-alt="{\displaystyle ({\sqrt {2}})^{\frac {0}{2}},\ ({\sqrt {2}})^{\frac {1}{2}},\ ({\sqrt {2}})^{\frac {2}{2}},\ ({\sqrt {2}})^{\frac {3}{2}},\ ({\sqrt {2}})^{\frac {4}{2}},\ \ldots }" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  The steps in a third stop (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄3 EV) series would be <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\sqrt {2}})^{\frac {0}{3}},\ ({\sqrt {2}})^{\frac {1}{3}},\ ({\sqrt {2}})^{\frac {2}{3}},\ ({\sqrt {2}})^{\frac {3}{3}},\ ({\sqrt {2}})^{\frac {4}{3}},\ \ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\sqrt {2}})^{\frac {0}{3}},\ ({\sqrt {2}})^{\frac {1}{3}},\ ({\sqrt {2}})^{\frac {2}{3}},\ ({\sqrt {2}})^{\frac {3}{3}},\ ({\sqrt {2}})^{\frac {4}{3}},\ \ldots }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fd219a2821d2e332e6228a2986c14cc1fc46641" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.4ex; height:4.009ex;" alt="{\displaystyle ({\sqrt {2}})^{\frac {0}{3}},\ ({\sqrt {2}})^{\frac {1}{3}},\ ({\sqrt {2}})^{\frac {2}{3}},\ ({\sqrt {2}})^{\frac {3}{3}},\ ({\sqrt {2}})^{\frac {4}{3}},\ \ldots }"></noscript><span class="lazy-image-placeholder" style="width: 44.4ex;height: 4.009ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fd219a2821d2e332e6228a2986c14cc1fc46641" data-alt="{\displaystyle ({\sqrt {2}})^{\frac {0}{3}},\ ({\sqrt {2}})^{\frac {1}{3}},\ ({\sqrt {2}})^{\frac {2}{3}},\ ({\sqrt {2}})^{\frac {3}{3}},\ ({\sqrt {2}})^{\frac {4}{3}},\ \ldots }" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  As in the earlier DIN and ASA film-speed standards, the ISO speed is defined only in one-third stop increments, and shutter speeds of digital cameras are commonly on the same scale in reciprocal seconds. A portion of the ISO range is the sequence <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ldots 16/13^{\circ },\ 20/14^{\circ },\ 25/15^{\circ },\ 32/16^{\circ },\ 40/17^{\circ },\ 50/18^{\circ },\ 64/19^{\circ },\ 80/20^{\circ },\ 100/21^{\circ },\ 125/22^{\circ },\ \ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>…</mo> <mn>16</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>13</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>20</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>14</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>15</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>32</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>16</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>40</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>17</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>50</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>18</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>64</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>19</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>80</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>20</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>100</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>21</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mn>125</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>22</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ldots 16/13^{\circ },\ 20/14^{\circ },\ 25/15^{\circ },\ 32/16^{\circ },\ 40/17^{\circ },\ 50/18^{\circ },\ 64/19^{\circ },\ 80/20^{\circ },\ 100/21^{\circ },\ 125/22^{\circ },\ \ldots }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/082f9935e717c1042b560fb3267f6988cd80cb23" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:93.357ex; height:2.843ex;" alt="{\displaystyle \ldots 16/13^{\circ },\ 20/14^{\circ },\ 25/15^{\circ },\ 32/16^{\circ },\ 40/17^{\circ },\ 50/18^{\circ },\ 64/19^{\circ },\ 80/20^{\circ },\ 100/21^{\circ },\ 125/22^{\circ },\ \ldots }"></noscript><span class="lazy-image-placeholder" style="width: 93.357ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/082f9935e717c1042b560fb3267f6988cd80cb23" data-alt="{\displaystyle \ldots 16/13^{\circ },\ 20/14^{\circ },\ 25/15^{\circ },\ 32/16^{\circ },\ 40/17^{\circ },\ 50/18^{\circ },\ 64/19^{\circ },\ 80/20^{\circ },\ 100/21^{\circ },\ 125/22^{\circ },\ \ldots }" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  while shutter speeds in reciprocal seconds have a few conventional differences in their numbers (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄15, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄30, and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄60 second instead of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄16, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄32, and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄64). In practice the maximum aperture of a lens is often not an <a href="/wiki/Integer" title="Integer">integral</a> power of √2 (i.e., √2 to the power of a whole number), in which case it is usually a half or third stop above or below an integral power of √2. Modern electronically controlled interchangeable lenses, such as those used for SLR cameras, have f-stops specified internally in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄8-stop increments, so the cameras' <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄3-stop settings are approximated by the nearest <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄8-stop setting in the lens.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading4"><h4 id="Standard_full-stop_f-number_scale">Standard full-stop f-number scale</h4> <a role="button" href="/w/index.php?title=F-number&action=edit&section=4" title="Edit section: Standard full-stop f-number scale" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Including <a href="/wiki/APEX_system" title="APEX system">aperture value</a> AV: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N={\sqrt {2^{\text{AV}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>AV</mtext> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N={\sqrt {2^{\text{AV}}}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50b7a9af47042c2056a94aa78a2c63c080b26356" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.346ex; height:3.509ex;" alt="{\displaystyle N={\sqrt {2^{\text{AV}}}}}"></noscript><span class="lazy-image-placeholder" style="width: 11.346ex;height: 3.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50b7a9af47042c2056a94aa78a2c63c080b26356" data-alt="{\displaystyle N={\sqrt {2^{\text{AV}}}}}" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  Conventional and calculated f-numbers, full-stop series: <table class="wikitable" style="text-align:center"> <tbody><tr> <th scope="row">AV </th> <td>−2</td> <td>−1</td> <td>0</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> <td>14</td> <td>15</td> <td>16 </td></tr> <tr bgcolor="#CCFFCD"> <th scope="row">N </th> <td>0.5</td> <td>0.7</td> <td>1.0</td> <td>1.4</td> <td>2</td> <td>2.8</td> <td>4</td> <td>5.6</td> <td>8</td> <td>11</td> <td>16</td> <td>22</td> <td>32</td> <td>45</td> <td>64</td> <td>90</td> <td>128</td> <td>180</td> <td>256 </td></tr> <tr> <th scope="row">calculated </th> <td>0.5</td> <td>0.707...</td> <td>1.0</td> <td>1.414...</td> <td>2.0</td> <td>2.828...</td> <td>4.0</td> <td>5.657...</td> <td>8.0</td> <td>11.31...</td> <td>16.0</td> <td>22.62...</td> <td>32.0</td> <td>45.25...</td> <td>64.0</td> <td>90.51...</td> <td>128.0</td> <td>181.02...</td> <td>256.0 </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Typical_one-half-stop_f-number_scale">Typical one-half-stop f-number scale</h4> <a role="button" href="/w/index.php?title=F-number&action=edit&section=5" title="Edit section: Typical one-half-stop f-number scale" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th scope="row">AV </th> <td>−1</td> <td>−<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄2</td> <td>0</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄2</td> <td>1</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1+1⁄2</td> <td>2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2+1⁄2</td> <td>3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">3+1⁄2</td> <td>4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">4+1⁄2</td> <td>5</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">5+1⁄2</td> <td>6</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">6+1⁄2</td> <td>7</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">7+1⁄2</td> <td>8</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">8+1⁄2</td> <td>9</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">9+1⁄2</td> <td>10</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">10+1⁄2</td> <td>11</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">11+1⁄2</td> <td>12</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">12+1⁄2</td> <td>13</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">13+1⁄2</td> <td>14 </td></tr> <tr bgcolor="#FFFFCC"> <th scope="row">N </th> <td style="background:#CCFFCC;">0.7</td> <td>0.8</td> <td style="background:#CCFFCC;">1.0</td> <td>1.2</td> <td style="background:#CCFFCC;">1.4</td> <td>1.7</td> <td style="background:#CCFFCC;">2</td> <td>2.4</td> <td style="background:#CCFFCC;">2.8</td> <td>3.3</td> <td style="background:#CCFFCC;">4</td> <td>4.8</td> <td style="background:#CCFFCC;">5.6</td> <td>6.7</td> <td style="background:#CCFFCC;">8</td> <td>9.5</td> <td style="background:#CCFFCC;">11</td> <td>13</td> <td style="background:#CCFFCC;">16</td> <td>19</td> <td style="background:#CCFFCC;">22</td> <td>27</td> <td style="background:#CCFFCC;">32</td> <td>38</td> <td style="background:#CCFFCC;">45</td> <td>54</td> <td style="background:#CCFFCC;">64</td> <td>76</td> <td style="background:#CCFFCC;">90</td> <td>107</td> <td style="background:#CCFFCC;">128 </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Typical_one-third-stop_f-number_scale">Typical one-third-stop f-number scale</h4> <a role="button" href="/w/index.php?title=F-number&action=edit&section=6" title="Edit section: Typical one-third-stop f-number scale" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th scope="row">AV </th> <td>−1</td> <td>−<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2⁄3</td> <td>−<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄3</td> <td>0</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2⁄3</td> <td>1</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1+2⁄3</td> <td>2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2+2⁄3</td> <td>3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">3+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">3+2⁄3</td> <td>4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">4+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">4+2⁄3</td> <td>5</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">5+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">5+2⁄3</td> <td>6</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">6+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">6+2⁄3</td> <td>7</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">7+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">7+2⁄3</td> <td>8</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">8+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">8+2⁄3</td> <td>9</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">9+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">9+2⁄3</td> <td>10</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">10+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">10+2⁄3</td> <td>11</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">11+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">11+2⁄3</td> <td>12</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">12+1⁄3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">12+2⁄3</td> <td>13 </td></tr> <tr bgcolor="#e5d1cb"> <th scope="row">N </th> <td style="background:#CCFFCC;">0.7</td> <td>0.8</td> <td>0.9</td> <td style="background:#CCFFCC;">1.0</td> <td>1.1</td> <td>1.2</td> <td style="background:#CCFFCC;">1.4</td> <td>1.6</td> <td>1.8</td> <td style="background:#CCFFCC;">2</td> <td>2.2</td> <td>2.5</td> <td style="background:#CCFFCC;">2.8</td> <td>3.2</td> <td>3.5</td> <td style="background:#CCFFCC;">4</td> <td>4.5</td> <td>5.0</td> <td style="background:#CCFFCC;">5.6</td> <td>6.3</td> <td>7.1</td> <td style="background:#CCFFCC;">8</td> <td>9</td> <td>10</td> <td style="background:#CCFFCC;">11</td> <td>13</td> <td>14</td> <td style="background:#CCFFCC;">16</td> <td>18</td> <td>20</td> <td style="background:#CCFFCC;">22</td> <td>25</td> <td>29</td> <td style="background:#CCFFCC;">32</td> <td>36</td> <td>40</td> <td style="background:#CCFFCC;">45</td> <td>51</td> <td>57</td> <td style="background:#CCFFCC;">64</td> <td>72</td> <td>80</td> <td style="background:#CCFFCC;">90 </td></tr></tbody></table> Sometimes the same number is included on several scales; for example, an aperture of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/1.2 may be used in either a half-stop<a href="#cite_note-7">[7]</a> or a one-third-stop system;<a href="#cite_note-8">[8]</a> sometimes <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/1.3 and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/3.2 and other differences are used for the one-third stop scale.<a href="#cite_note-9">[9]</a> <div class="mw-heading mw-heading4"><h4 id="Typical_one-quarter-stop_f-number_scale">Typical one-quarter-stop f-number scale</h4> <a role="button" href="/w/index.php?title=F-number&action=edit&section=7" title="Edit section: Typical one-quarter-stop f-number scale" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th scope="row">AV </th> <td>0</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">3⁄4</td> <td>1</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1+3⁄4</td> <td>2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">2+3⁄4</td> <td>3</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">3+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">3+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">3+3⁄4</td> <td>4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">4+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">4+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">4+3⁄4</td> <td>5 </td></tr> <tr bgcolor="#5D8AA8"> <th scope="row">N </th> <td style="background:#CCFFCC;">1.0</td> <td>1.1</td> <td style="background:#FFFFCC;">1.2</td> <td>1.3</td> <td style="background:#CCFFCC;">1.4</td> <td>1.5</td> <td style="background:#FFFFCC;">1.7</td> <td>1.8</td> <td style="background:#CCFFCC;">2</td> <td>2.2</td> <td style="background:#FFFFCC;">2.4</td> <td>2.6</td> <td style="background:#CCFFCC;">2.8</td> <td>3.1</td> <td style="background:#FFFFCC;">3.3</td> <td>3.7</td> <td style="background:#CCFFCC;">4</td> <td>4.4</td> <td style="background:#FFFFCC;">4.8</td> <td>5.2</td> <td style="background:#CCFFCC;">5.6 </td></tr></tbody></table> <table class="wikitable" style="text-align:center"> <tbody><tr> <th scope="row">AV </th> <td>5</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">5+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">5+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">5+3⁄4</td> <td>6</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">6+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">6+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">6+3⁄4</td> <td>7</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">7+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">7+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">7+3⁄4</td> <td>8</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">8+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">8+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">8+3⁄4</td> <td>9</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">9+1⁄4</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">9+1⁄2</td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">9+3⁄4</td> <td>10 </td></tr> <tr bgcolor="#5D8AA8"> <th scope="row">N </th> <td style="background:#CCFFCC;">5.6</td> <td>6.2</td> <td style="background:#FFFFCC;">6.7</td> <td>7.3</td> <td style="background:#CCFFCC;">8</td> <td>8.7</td> <td style="background:#FFFFCC;">9.5</td> <td>10</td> <td style="background:#CCFFCC;">11</td> <td>12</td> <td style="background:#FFFFCC;">14</td> <td>15</td> <td style="background:#CCFFCC;">16</td> <td>17</td> <td style="background:#FFFFCC;">19</td> <td>21</td> <td style="background:#CCFFCC;">22</td> <td>25</td> <td style="background:#FFFFCC;">27</td> <td>29</td> <td style="background:#CCFFCC;">32 </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="H-stop">H-stop</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=8" title="Edit section: H-stop" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> An H-stop (for hole, by convention written with capital letter H) is an f-number equivalent for effective exposure based on the area covered by the holes in the <a href="/wiki/Diffusion_disc" class="mw-redirect" title="Diffusion disc">diffusion discs</a> or <a href="/wiki/Sieve_aperture" class="mw-redirect" title="Sieve aperture">sieve aperture</a> found in <a href="/wiki/Rodenstock_Imagon" title="Rodenstock Imagon">Rodenstock Imagon</a> lenses. <div class="mw-heading mw-heading3"><h3 id="T-stop">T-stop</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=9" title="Edit section: T-stop" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A T-stop (for transmission stops, by convention written with capital letter T) is an f-number adjusted to account for light transmission efficiency (<a href="/wiki/Transmittance" title="Transmittance">transmittance</a>). A lens with a T-stop of N projects an image of the same brightness as an ideal lens with 100% transmittance and an f-number of N. A particular lens's T-stop, T, is given by dividing the f-number by the square root of the transmittance of that lens: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T={\frac {N}{\sqrt {\text{transmittance}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>N</mi> <msqrt> <mtext>transmittance</mtext> </msqrt> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {N}{\sqrt {\text{transmittance}}}}.}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00019bc9b6d403bb7254c8d787b62e27f40263c4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:22.253ex; height:6.176ex;" alt="{\displaystyle T={\frac {N}{\sqrt {\text{transmittance}}}}.}"></noscript><span class="lazy-image-placeholder" style="width: 22.253ex;height: 6.176ex;vertical-align: -2.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00019bc9b6d403bb7254c8d787b62e27f40263c4" data-alt="{\displaystyle T={\frac {N}{\sqrt {\text{transmittance}}}}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  For example, an <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2.0 lens with transmittance of 75% has a T-stop of 2.3: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T={\frac {2.0}{\sqrt {0.75}}}=2.309...}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2.0</mn> <msqrt> <mn>0.75</mn> </msqrt> </mfrac> </mrow> <mo>=</mo> <mn>2.309...</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {2.0}{\sqrt {0.75}}}=2.309...}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8ba69ffa38ca312ec95f5a5ebee2094b3e0d29e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:21.977ex; height:6.176ex;" alt="{\displaystyle T={\frac {2.0}{\sqrt {0.75}}}=2.309...}"></noscript><span class="lazy-image-placeholder" style="width: 21.977ex;height: 6.176ex;vertical-align: -2.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8ba69ffa38ca312ec95f5a5ebee2094b3e0d29e" data-alt="{\displaystyle T={\frac {2.0}{\sqrt {0.75}}}=2.309...}" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  Since real lenses have transmittances of less than 100%, a lens's T-stop number is always greater than its f-number.<a href="#cite_note-10">[10]</a> With 8% loss per air-glass surface on lenses without coating, <a href="/wiki/History_of_photographic_lens_design#Anti-reflection_coating" title="History of photographic lens design">multicoating</a> of lenses is the key in lens design to decrease transmittance losses of lenses. Some reviews of lenses do measure the T-stop or transmission rate in their benchmarks.<a href="#cite_note-11">[11]</a><a href="#cite_note-12">[12]</a> T-stops are sometimes used instead of f-numbers to more accurately determine exposure, particularly when using external <a href="/wiki/Light_meter" title="Light meter">light meters</a>.<a href="#cite_note-KMPCF-13">[13]</a> Lens transmittances of 60%–95% are typical.<a href="#cite_note-14">[14]</a> T-stops are often used in cinematography, where many images are seen in rapid succession and even small changes in exposure will be noticeable. Cinema camera lenses are typically calibrated in T-stops instead of f-numbers.<a href="#cite_note-KMPCF-13">[13]</a> In still photography, without the need for rigorous consistency of all lenses and cameras used, slight differences in exposure are less important; however, T-stops are still used in some kinds of special-purpose lenses such as <a href="/wiki/Smooth_Trans_Focus" title="Smooth Trans Focus">Smooth Trans Focus</a> lenses by <a href="/wiki/Minolta" title="Minolta">Minolta</a> and <a href="/wiki/Sony" title="Sony">Sony</a>. <div class="mw-heading mw-heading3"><h3 id="ASA/ISO_numbers">ASA/ISO numbers</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=10" title="Edit section: ASA/ISO numbers" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <a href="/wiki/Photographic_film" title="Photographic film">Photographic film</a>'s and electronic camera sensor's <a href="/wiki/Photosensitivity" title="Photosensitivity">sensitivity to light</a> is often specified using <a href="/wiki/Film_speed" title="Film speed">ASA/ISO numbers</a>. Both systems have a linear number where a doubling of sensitivity is represented by a doubling of the number, and a logarithmic number. In the ISO system, a 3° increase in the logarithmic number corresponds to a doubling of sensitivity. Doubling or halving the sensitivity is equal to a difference of one T-stop in terms of light transmittance. <div class="mw-heading mw-heading3"><h3 id="Gain">Gain</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=11" title="Edit section: Gain" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Panasonic_Iris-Gain_relationship.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/en/thumb/0/09/Panasonic_Iris-Gain_relationship.png/300px-Panasonic_Iris-Gain_relationship.png" decoding="async" width="300" height="35" class="mw-file-element" data-file-width="919" data-file-height="108"></noscript><span class="lazy-image-placeholder" style="width: 300px;height: 35px;" data-src="//upload.wikimedia.org/wikipedia/en/thumb/0/09/Panasonic_Iris-Gain_relationship.png/300px-Panasonic_Iris-Gain_relationship.png" data-width="300" data-height="35" data-srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/09/Panasonic_Iris-Gain_relationship.png/450px-Panasonic_Iris-Gain_relationship.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/0/09/Panasonic_Iris-Gain_relationship.png/600px-Panasonic_Iris-Gain_relationship.png 2x" data-class="mw-file-element"> </a><figcaption>Iris/Gain relationship on Panasonic camcorders as described in the HC-V785 operating manual</figcaption></figure> Most electronic cameras allow to amplify the signal coming from the pickup element. This amplification is usually called <a href="/wiki/Gain_(electronics)" title="Gain (electronics)">gain</a> and is measured in decibels. Every 6 dB of gain is equivalent to one T-stop in terms of light transmittance. Many camcorders have a unified control over the lens f-number and gain. In this case, starting from zero gain and fully open iris, one can either increase f-number by reducing the iris size while gain remains zero, or one can increase gain while iris remains fully open. <div class="mw-heading mw-heading3"><h3 id="Sunny_16_rule">Sunny 16 rule</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=12" title="Edit section: Sunny 16 rule" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> An example of the use of f-numbers in photography is the <a href="/wiki/Sunny_16_rule" title="Sunny 16 rule">sunny 16 rule</a>: an approximately correct exposure will be obtained on a sunny day by using an aperture of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/16 and the shutter speed closest to the <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">reciprocal</a> of the ISO speed of the film; for example, using ISO 200 film, an aperture of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/16 and a shutter speed of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄200 second. The f-number may then be adjusted downwards for situations with lower light. Selecting a lower f-number is "opening up" the lens. Selecting a higher f-number is "closing" or "stopping down" the lens. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><h2 id="Effects_on_image_sharpness">Effects on image sharpness</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=13" title="Edit section: Effects on image sharpness" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Jonquil_flowers_merged.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Jonquil_flowers_merged.jpg/400px-Jonquil_flowers_merged.jpg" decoding="async" width="400" height="264" class="mw-file-element" data-file-width="1600" data-file-height="1054"></noscript><span class="lazy-image-placeholder" style="width: 400px;height: 264px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Jonquil_flowers_merged.jpg/400px-Jonquil_flowers_merged.jpg" data-width="400" data-height="264" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Jonquil_flowers_merged.jpg/600px-Jonquil_flowers_merged.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Jonquil_flowers_merged.jpg/800px-Jonquil_flowers_merged.jpg 2x" data-class="mw-file-element"> </a><figcaption>Comparison of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/32 (top-left half) and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/5 (bottom-right half)</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Blumen_im_Sommer.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Blumen_im_Sommer.jpg/400px-Blumen_im_Sommer.jpg" decoding="async" width="400" height="77" class="mw-file-element" data-file-width="5616" data-file-height="1080"></noscript><span class="lazy-image-placeholder" style="width: 400px;height: 77px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Blumen_im_Sommer.jpg/400px-Blumen_im_Sommer.jpg" data-width="400" data-height="77" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Blumen_im_Sommer.jpg/600px-Blumen_im_Sommer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Blumen_im_Sommer.jpg/800px-Blumen_im_Sommer.jpg 2x" data-class="mw-file-element"> </a><figcaption>Shallow focus with a wide open lens</figcaption></figure> <a href="/wiki/Depth_of_field" title="Depth of field">Depth of field</a> increases with f-number, as illustrated in the image here. This means that photographs taken with a low f-number (large aperture) will tend to have subjects at one distance in focus, with the rest of the image (nearer and farther elements) out of focus. This is frequently used for <a href="/wiki/Nature_photography" title="Nature photography">nature photography</a> and <a href="/wiki/Portrait_photography" title="Portrait photography">portraiture</a> because background blur (the aesthetic quality known as '<a href="/wiki/Bokeh" title="Bokeh">bokeh</a>') can be aesthetically pleasing and puts the viewer's focus on the main subject in the foreground. The <a href="/wiki/Depth_of_field" title="Depth of field">depth of field</a> of an image produced at a given f-number is dependent on other parameters as well, including the <a href="/wiki/Focal_length" title="Focal length">focal length</a>, the subject distance, and the <a href="/wiki/Film_format" title="Film format">format</a> of the film or sensor used to capture the image. Depth of field can be described as depending on just angle of view, subject distance, and <a href="/wiki/Entrance_pupil" title="Entrance pupil">entrance pupil</a> diameter (as in <a href="/wiki/Moritz_von_Rohr" title="Moritz von Rohr">von Rohr's method</a>). As a result, smaller formats will have a deeper field than larger formats at the same f-number for the same distance of focus and same <a href="/wiki/Angle_of_view" class="mw-redirect" title="Angle of view">angle of view</a> since a smaller format requires a shorter focal length (wider angle lens) to produce the same angle of view, and depth of field increases with shorter focal lengths. Therefore, reduced–depth-of-field effects will require smaller f-numbers (and thus potentially more difficult or complex optics) when using small-format cameras than when using larger-format cameras. Beyond focus, image sharpness is related to f-number through two different optical effects: <a href="/wiki/Optical_aberration" title="Optical aberration">aberration</a>, due to imperfect lens design, and <a href="/wiki/Diffraction" title="Diffraction">diffraction</a> which is due to the wave nature of light.<a href="#cite_note-15">[15]</a> The blur-optimal f-stop varies with the lens design. For modern standard lenses having 6 or 7 elements, the <a href="/wiki/Sharpness_(visual)" class="mw-redirect" title="Sharpness (visual)">sharpest</a> image is often obtained around <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/5.6–<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8, while for older standard lenses having only 4 elements (<a href="/wiki/Zeiss_Tessar" class="mw-redirect" title="Zeiss Tessar">Tessar formula</a>) stopping to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/11 will give the sharpest image.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] The larger number of elements in modern lenses allow the designer to compensate for aberrations, allowing the lens to give better pictures at lower f-numbers. At small apertures, depth of field and aberrations are improved, but <a href="/wiki/Diffraction" title="Diffraction">diffraction</a> creates more spreading of the light, causing blur. Light falloff is also sensitive to f-stop. Many wide-angle lenses will show a significant light falloff (<a href="/wiki/Vignetting" title="Vignetting">vignetting</a>) at the edges for large apertures. <a href="/wiki/Photojournalist" class="mw-redirect" title="Photojournalist">Photojournalists</a> have a saying, "<a href="/wiki/F/8_and_be_there" title="F/8 and be there"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8 and be there</a>", meaning that being on the scene is more important than worrying about technical details. Practically, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8 (in 35 mm and larger formats) allows adequate depth of field and sufficient lens speed for a decent base exposure in most daylight situations.<a href="#cite_note-16">[16]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><h2 id="Human_eye">Human eye</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=14" title="Edit section: Human eye" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Pupillary_light_reflex.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Pupillary_light_reflex.jpg/382px-Pupillary_light_reflex.jpg" decoding="async" width="382" height="127" class="mw-file-element" data-file-width="1800" data-file-height="600"></noscript><span class="lazy-image-placeholder" style="width: 382px;height: 127px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Pupillary_light_reflex.jpg/382px-Pupillary_light_reflex.jpg" data-width="382" data-height="127" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Pupillary_light_reflex.jpg/573px-Pupillary_light_reflex.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Pupillary_light_reflex.jpg/764px-Pupillary_light_reflex.jpg 2x" data-class="mw-file-element"> </a><figcaption>The human pupil in its constricted (3 mm) and fully dilated (9 mm) states. At 9 mm, the effective f-number is approximately <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/1.6.</figcaption></figure> Computing the f-number of the <a href="/wiki/Human_eye" title="Human eye">human eye</a> involves computing the physical aperture and focal length of the eye. Typically, the pupil can dilate to be as large as 6–7 mm in darkness, which translates into the maximal physical aperture. Some individuals' pupils can dilate to over 9 mm wide. The f-number of the human eye varies from about <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8.3 in a very brightly lit place to about <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/2.1 in the dark.<a href="#cite_note-17">[17]</a> Computing the focal length requires that the light-refracting properties of the liquids in the eye be taken into account. Treating the eye as an ordinary air-filled camera and lens results in an incorrect focal length and f-number. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><h2 id="Focal_ratio_in_telescopes">Focal ratio in telescopes</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=15" title="Edit section: Focal ratio in telescopes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Focal_ratio.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Focal_ratio.svg/250px-Focal_ratio.svg.png" decoding="async" width="250" height="133" class="mw-file-element" data-file-width="643" data-file-height="341"></noscript><span class="lazy-image-placeholder" style="width: 250px;height: 133px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Focal_ratio.svg/250px-Focal_ratio.svg.png" data-width="250" data-height="133" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Focal_ratio.svg/375px-Focal_ratio.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Focal_ratio.svg/500px-Focal_ratio.svg.png 2x" data-class="mw-file-element"> </a><figcaption>Diagram of the <a href="/wiki/Focal_ratio" class="mw-redirect" title="Focal ratio">focal ratio</a> of a simple optical system where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></noscript><span class="lazy-image-placeholder" style="width: 1.279ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" data-alt="{\displaystyle f}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the <a href="/wiki/Focal_length" title="Focal length">focal length</a> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></noscript><span class="lazy-image-placeholder" style="width: 1.924ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" data-alt="{\displaystyle D}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the diameter of the <a href="/wiki/Objective_(optics)" title="Objective (optics)">objective</a></figcaption></figure> In astronomy, the f-number is commonly referred to as the focal ratio (or f-ratio) notated as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></noscript><span class="lazy-image-placeholder" style="width: 2.064ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" data-alt="{\displaystyle N}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . It is still defined as the <a href="/wiki/Focal_length" title="Focal length">focal length</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></noscript><span class="lazy-image-placeholder" style="width: 1.279ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" data-alt="{\displaystyle f}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  of an <a href="/wiki/Objective_(optics)" title="Objective (optics)">objective</a> divided by its diameter <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></noscript><span class="lazy-image-placeholder" style="width: 1.924ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" data-alt="{\displaystyle D}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  or by the diameter of an <a href="/wiki/Aperture" title="Aperture">aperture</a> stop in the system: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N={\frac {f}{D}}\quad {\xrightarrow {\times D}}\quad f=ND}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <mi>D</mi> </mfrac> </mrow> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mo>×</mo> <mi>D</mi> </mpadded> </mover> </mrow> <mspace width="1em"></mspace> <mi>f</mi> <mo>=</mo> <mi>N</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N={\frac {f}{D}}\quad {\xrightarrow {\times D}}\quad f=ND}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0526dab2e8782c7a32e292f4f05cd562adcddf61" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:24.895ex; height:5.343ex;" alt="{\displaystyle N={\frac {f}{D}}\quad {\xrightarrow {\times D}}\quad f=ND}"></noscript><span class="lazy-image-placeholder" style="width: 24.895ex;height: 5.343ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0526dab2e8782c7a32e292f4f05cd562adcddf61" data-alt="{\displaystyle N={\frac {f}{D}}\quad {\xrightarrow {\times D}}\quad f=ND}" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  Even though the principles of focal ratio are always the same, the application to which the principle is put can differ. In <a href="/wiki/Photography" title="Photography">photography</a> the focal ratio varies the focal-plane illuminance (or optical power per unit area in the image) and is used to control variables such as <a href="/wiki/Depth_of_field" title="Depth of field">depth of field</a>. When using an <a href="/wiki/Optical_telescope" title="Optical telescope">optical telescope</a> in astronomy, there is no depth of field issue, and the brightness of stellar point sources in terms of total optical power (not divided by area) is a function of absolute aperture area only, independent of focal length. The focal length controls the <a href="/wiki/Field_of_view#Astronomy" title="Field of view">field of view</a> of the instrument and the scale of the image that is presented at the focal plane to an <a href="/wiki/Eyepiece" title="Eyepiece">eyepiece</a>, film plate, or <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">CCD</a>. For example, the <a href="/wiki/Southern_Astrophysical_Research_Telescope" title="Southern Astrophysical Research Telescope">SOAR</a> 4-meter telescope has a small field of view (about <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/16) which is useful for stellar studies. The <a href="/wiki/Large_Synoptic_Survey_Telescope" class="mw-redirect" title="Large Synoptic Survey Telescope">LSST</a> 8.4 m telescope, which will cover the entire sky every three days, has a very large field of view. Its short 10.3 m focal length (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/1.2) is made possible by an error correction system which includes secondary and tertiary mirrors, a three element refractive system and active mounting and optics.<a href="#cite_note-RefDesign-18">[18]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"><h2 id="Camera_equation_(G#)">Camera equation (G#)</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=16" title="Edit section: Camera equation (G#)" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-6 collapsible-block" id="mf-section-6"> The camera equation, or G#, is the ratio of the <a href="/wiki/Radiance" title="Radiance">radiance</a> reaching the camera sensor to the <a href="/wiki/Irradiance" title="Irradiance">irradiance</a> on the focal plane of the <a href="/wiki/Camera_lens" title="Camera lens">camera lens</a>:<a href="#cite_note-g-number-19">[19]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G\#={\frac {1+4N^{2}}{\tau \pi }}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi mathvariant="normal">#</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mn>4</mn> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>τ</mi> <mi>π</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G\#={\frac {1+4N^{2}}{\tau \pi }}\,,}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8db3b338fda85ee2bcbeba6563e414232aec766e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.074ex; height:5.676ex;" alt="{\displaystyle G\#={\frac {1+4N^{2}}{\tau \pi }}\,,}"></noscript><span class="lazy-image-placeholder" style="width: 17.074ex;height: 5.676ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8db3b338fda85ee2bcbeba6563e414232aec766e" data-alt="{\displaystyle G\#={\frac {1+4N^{2}}{\tau \pi }}\,,}" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  where τ is the transmission coefficient of the lens, and the units are in inverse <a href="/wiki/Steradian" title="Steradian">steradians</a> (sr−1). </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"><h2 id="Working_f-number">Working f-number</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=17" title="Edit section: Working f-number" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-7 collapsible-block" id="mf-section-7"> The f-number accurately describes the light-gathering ability of a lens only for objects an infinite distance away.<a href="#cite_note-Greivenkamp-20">[20]</a> This limitation is typically ignored in photography, where f-number is often used regardless of the distance to the object. In <a href="/wiki/Optical_design" class="mw-redirect" title="Optical design">optical design</a>, an alternative is often needed for systems where the object is not far from the lens. In these cases the working f-number is used. The working f-number Nw is given by:<a href="#cite_note-Greivenkamp-20">[20]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{w}\approx {1 \over 2\mathrm {NA} _{i}}\approx \left(1+{\frac {|m|}{P}}\right)N\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> </mrow> </msub> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>≈</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mi>P</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mi>N</mi> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{w}\approx {1 \over 2\mathrm {NA} _{i}}\approx \left(1+{\frac {|m|}{P}}\right)N\,,}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d66d162ff02d11d09eceed71542fb5a35fad12bc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.835ex; height:6.343ex;" alt="{\displaystyle N_{w}\approx {1 \over 2\mathrm {NA} _{i}}\approx \left(1+{\frac {|m|}{P}}\right)N\,,}"></noscript><span class="lazy-image-placeholder" style="width: 30.835ex;height: 6.343ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d66d162ff02d11d09eceed71542fb5a35fad12bc" data-alt="{\displaystyle N_{w}\approx {1 \over 2\mathrm {NA} _{i}}\approx \left(1+{\frac {|m|}{P}}\right)N\,,}" data-class="mwe-math-fallback-image-display mw-invert skin-invert">  where N is the uncorrected f-number, NAi is the image-space <a href="/wiki/Numerical_aperture" title="Numerical aperture">numerical aperture</a> of the lens, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |m|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |m|}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9aa0b9c6f0a110ae299bf81e924412842ce2b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.334ex; height:2.843ex;" alt="{\displaystyle |m|}"></noscript><span class="lazy-image-placeholder" style="width: 3.334ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9aa0b9c6f0a110ae299bf81e924412842ce2b12" data-alt="{\displaystyle |m|}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a> of the lens's <a href="/wiki/Magnification" title="Magnification">magnification</a> for an object a particular distance away, and P is the <a href="/wiki/Pupil_magnification" title="Pupil magnification">pupil magnification</a>. Since the pupil magnification is seldom known it is often assumed to be 1, which is the correct value for all symmetric lenses. In photography this means that as one focuses closer, the lens's effective aperture becomes smaller, making the exposure darker. The working f-number is often described in photography as the f-number corrected for lens extensions by a <a href="/w/index.php?title=Bellows_factor&action=edit&redlink=1" class="new" title="Bellows factor (page does not exist)">bellows factor</a>. This is of particular importance in <a href="/wiki/Macro_photography" title="Macro photography">macro photography</a>. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"><h2 id="History">History</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=18" title="Edit section: History" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-8 collapsible-block" id="mf-section-8"> The system of f-numbers for specifying relative apertures evolved in the late nineteenth century, in competition with several other systems of aperture notation. <div class="mw-heading mw-heading3"><h3 id="Origins_of_relative_aperture">Origins of relative aperture</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=19" title="Edit section: Origins of relative aperture" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> In 1867, Sutton and Dawson defined "apertal ratio" as essentially the reciprocal of the modern f-number. In the following quote, an "apertal ratio" of "<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄24" is calculated as the ratio of 6 inches (150 mm) to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄4 inch (6.4 mm), corresponding to an <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/24 f-stop: <blockquote>In every lens there is, corresponding to a given apertal ratio (that is, the ratio of the diameter of the stop to the focal length), a certain distance of a near object from it, between which and infinity all objects are in equally good focus. For instance, in a single view lens of 6-inch focus, with a <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄4 in. stop (apertal ratio one-twenty-fourth), all objects situated at distances lying between 20 feet from the lens and an infinite distance from it (a fixed star, for instance) are in equally good focus. Twenty feet is therefore called the 'focal range' of the lens when this stop is used. The focal range is consequently the distance of the nearest object, which will be in good focus when the ground glass is adjusted for an extremely distant object. In the same lens, the focal range will depend upon the size of the diaphragm used, while in different lenses having the same apertal ratio the focal ranges will be greater as the focal length of the lens is increased. The terms 'apertal ratio' and 'focal range' have not come into general use, but it is very desirable that they should, in order to prevent ambiguity and circumlocution when treating of the properties of photographic lenses.<a href="#cite_note-Sutton-21">[21]</a></blockquote> In 1874, <a href="/wiki/John_Henry_Dallmeyer" title="John Henry Dallmeyer">John Henry Dallmeyer</a> called the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/N}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa5c2544725c51dfe75eea07ee1f487feb8664c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.389ex; height:2.843ex;" alt="{\displaystyle 1/N}"></noscript><span class="lazy-image-placeholder" style="width: 4.389ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa5c2544725c51dfe75eea07ee1f487feb8664c4" data-alt="{\displaystyle 1/N}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  the "intensity ratio" of a lens: <blockquote>The rapidity of a lens depends upon the relation or ratio of the aperture to the equivalent focus. To ascertain this, divide the equivalent focus by the diameter of the actual working aperture of the lens in question; and note down the quotient as the denominator with 1, or unity, for the numerator. Thus to find the ratio of a lens of 2 inches diameter and 6 inches focus, divide the focus by the aperture, or 6 divided by 2 equals 3; i.e., <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄3 is the intensity ratio.<a href="#cite_note-Dallmeyer-22">[22]</a></blockquote> Although he did not yet have access to <a href="/wiki/Ernst_Abbe" title="Ernst Abbe">Ernst Abbe</a>'s theory of stops and pupils,<a href="#cite_note-23">[23]</a> which was made widely available by <a href="/wiki/Siegfried_Czapski" title="Siegfried Czapski">Siegfried Czapski</a> in 1893,<a href="#cite_note-Czapski-24">[24]</a> Dallmeyer knew that his working aperture was not the same as the physical diameter of the aperture stop: <blockquote>It must be observed, however, that in order to find the real intensity ratio, the diameter of the actual working aperture must be ascertained. This is easily accomplished in the case of single lenses, or for double combination lenses used with the full opening, these merely requiring the application of a pair of compasses or rule; but when double or triple-combination lenses are used, with stops inserted between the combinations, it is somewhat more troublesome; for it is obvious that in this case the diameter of the stop employed is not the measure of the actual pencil of light transmitted by the front combination. To ascertain this, focus for a distant object, remove the focusing screen and replace it by the collodion slide, having previously inserted a piece of cardboard in place of the prepared plate. Make a small round hole in the centre of the cardboard with a piercer, and now remove to a darkened room; apply a candle close to the hole, and observe the illuminated patch visible upon the front combination; the diameter of this circle, carefully measured, is the actual working aperture of the lens in question for the particular stop employed.<a href="#cite_note-Dallmeyer-22">[22]</a></blockquote> This point is further emphasized by Czapski in 1893.<a href="#cite_note-Czapski-24">[24]</a> According to an English review of his book, in 1894, "The necessity of clearly distinguishing between effective aperture and diameter of physical stop is strongly insisted upon."<a href="#cite_note-25">[25]</a> J. H. Dallmeyer's son, <a href="/wiki/Thomas_Rudolphus_Dallmeyer" title="Thomas Rudolphus Dallmeyer">Thomas Rudolphus Dallmeyer</a>, inventor of the telephoto lens, followed the intensity ratio terminology in 1899.<a href="#cite_note-26">[26]</a> <div class="mw-heading mw-heading3"><h3 id="Aperture_numbering_systems">Aperture numbering systems</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=20" title="Edit section: Aperture numbering systems" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:No1-A_Autographic_Kodak_Jr.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/No1-A_Autographic_Kodak_Jr.jpg/220px-No1-A_Autographic_Kodak_Jr.jpg" decoding="async" width="220" height="352" class="mw-file-element" data-file-width="800" data-file-height="1279"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 352px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/No1-A_Autographic_Kodak_Jr.jpg/220px-No1-A_Autographic_Kodak_Jr.jpg" data-width="220" data-height="352" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/No1-A_Autographic_Kodak_Jr.jpg/330px-No1-A_Autographic_Kodak_Jr.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bb/No1-A_Autographic_Kodak_Jr.jpg/440px-No1-A_Autographic_Kodak_Jr.jpg 2x" data-class="mw-file-element"> </a><figcaption> A 1922 Kodak with aperture marked in U.S. stops. An f-number conversion chart has been added by the user.</figcaption></figure> At the same time, there were a number of aperture numbering systems designed with the goal of making exposure times vary in direct or inverse proportion with the aperture, rather than with the square of the f-number or inverse square of the apertal ratio or intensity ratio. But these systems all involved some arbitrary constant, as opposed to the simple ratio of focal length and diameter. For example, the Uniform System (U.S.) of apertures was adopted as a standard by the <a href="/wiki/Royal_Photographic_Society" title="Royal Photographic Society">Photographic Society of Great Britain</a> in the 1880s. Bothamley in 1891 said "The stops of all the best makers are now arranged according to this system."<a href="#cite_note-27">[27]</a> U.S. 16 is the same aperture as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/16, but apertures that are larger or smaller by a full stop use doubling or halving of the U.S. number, for example <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/11 is U.S. 8 and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8 is U.S. 4. The exposure time required is directly proportional to the U.S. number. <a href="/wiki/Eastman_Kodak" class="mw-redirect" title="Eastman Kodak">Eastman Kodak</a> used U.S. stops on many of their cameras at least in the 1920s. By 1895, Hodges contradicts Bothamley, saying that the f-number system has taken over: "This is called the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/x system, and the diaphragms of all modern lenses of good construction are so marked."<a href="#cite_note-28">[28]</a> Here is the situation as seen in 1899: <figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/File:Diaphragm_Numbers.gif" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Diaphragm_Numbers.gif/823px-Diaphragm_Numbers.gif" decoding="async" width="823" height="477" class="mw-file-element" data-file-width="1646" data-file-height="954"></noscript><span class="lazy-image-placeholder" style="width: 823px;height: 477px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Diaphragm_Numbers.gif/823px-Diaphragm_Numbers.gif" data-width="823" data-height="477" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Diaphragm_Numbers.gif/1235px-Diaphragm_Numbers.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/5/55/Diaphragm_Numbers.gif 2x" data-class="mw-file-element"> </a><figcaption></figcaption></figure> Piper in 1901<a href="#cite_note-29">[29]</a> discusses five different systems of aperture marking: the old and new <a href="/wiki/Carl_Zeiss" title="Carl Zeiss">Zeiss</a> systems based on actual intensity (proportional to reciprocal square of the f-number); and the U.S., C.I., and Dallmeyer systems based on exposure (proportional to square of the f-number). He calls the f-number the "ratio number", "aperture ratio number", and "ratio aperture". He calls expressions like <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8 the "fractional diameter" of the aperture, even though it is literally equal to the "absolute diameter" which he distinguishes as a different term. He also sometimes uses expressions like "an aperture of f 8" without the division indicated by the slash. Beck and Andrews in 1902 talk about the Royal Photographic Society standard of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/4, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/5.6, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/8, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1207775266">f/11.3, etc.<a href="#cite_note-30">[30]</a> The R.P.S. had changed their name and moved off of the U.S. system some time between 1895 and 1902. <div class="mw-heading mw-heading3"><h3 id="Typographical_standardization">Typographical standardization</h3> <a role="button" href="/w/index.php?title=F-number&action=edit&section=21" title="Edit section: Typographical standardization" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Yashica-D_front.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Yashica-D_front.jpg/220px-Yashica-D_front.jpg" decoding="async" width="220" height="340" class="mw-file-element" data-file-width="1297" data-file-height="2003"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 340px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Yashica-D_front.jpg/220px-Yashica-D_front.jpg" data-width="220" data-height="340" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Yashica-D_front.jpg/330px-Yashica-D_front.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Yashica-D_front.jpg/440px-Yashica-D_front.jpg 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Yashica#TLRs" title="Yashica">Yashica-D TLR</a> camera front view. This is one of the few cameras that actually says "F-NUMBER" on it.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Yashica-D_top.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Yashica-D_top.jpg/220px-Yashica-D_top.jpg" decoding="async" width="220" height="136" class="mw-file-element" data-file-width="1396" data-file-height="862"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 136px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Yashica-D_top.jpg/220px-Yashica-D_top.jpg" data-width="220" data-height="136" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Yashica-D_top.jpg/330px-Yashica-D_top.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Yashica-D_top.jpg/440px-Yashica-D_top.jpg 2x" data-class="mw-file-element"> </a><figcaption>From the top, the Yashica-D's aperture setting window uses the "f:" notation. The aperture is continuously variable with no "stops".</figcaption></figure> By 1920, the term f-number appeared in books both as F number and f/number. In modern publications, the forms f-number and f number are more common, though the earlier forms, as well as F-number are still found in a few books; not uncommonly, the initial lower-case f in f-number or f/number is set in a hooked italic form: ƒ.<a href="#cite_note-31">[31]</a> Notations for f-numbers were also quite variable in the early part of the twentieth century. They were sometimes written with a capital F,<a href="#cite_note-32">[32]</a> sometimes with a dot (period) instead of a slash,<a href="#cite_note-33">[33]</a> and sometimes set as a vertical fraction.<a href="#cite_note-34">[34]</a> The 1961 <a href="/wiki/American_National_Standards_Institute" title="American National Standards Institute">ASA</a> standard PH2.12-1961 American Standard General-Purpose Photographic Exposure Meters (Photoelectric Type) specifies that "The symbol for relative apertures shall be ƒ/ or ƒ: followed by the effective ƒ-number." They show the hooked italic 'ƒ' not only in the symbol, but also in the term f-number, which today is more commonly set in an ordinary non-italic face. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(9)"><h2 id="See_also">See also</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=22" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-9 collapsible-block" id="mf-section-9"> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output 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class="portalbox-entry"><noscript><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Video-x-generic.svg/28px-Video-x-generic.svg.png" decoding="async" width="28" height="28" class="mw-file-element" data-file-width="48" data-file-height="48"></noscript><span class="lazy-image-placeholder" style="width: 28px;height: 28px;" data-src="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Video-x-generic.svg/28px-Video-x-generic.svg.png" data-alt="" data-width="28" data-height="28" data-srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Video-x-generic.svg/42px-Video-x-generic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e7/Video-x-generic.svg/56px-Video-x-generic.svg.png 2x" data-class="mw-file-element"> <a href="/wiki/Portal:Film" title="Portal:Film">Film portal</a></li></ul> <ul><li><a href="/wiki/Circle_of_confusion" title="Circle of confusion">Circle of confusion</a></li> <li><a href="/wiki/Group_f/64" title="Group f/64">Group f/64</a></li> <li><a href="/wiki/Photographic_lens_design" title="Photographic lens design">Photographic lens design</a></li> <li><a href="/wiki/Pinhole_camera" title="Pinhole camera">Pinhole camera</a></li> <li><a href="/wiki/Preferred_number" title="Preferred number">Preferred number</a></li></ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(10)"><h2 id="References">References</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=23" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-10 collapsible-block" id="mf-section-10"> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-ReferenceA-1">^ <a href="#cite_ref-ReferenceA_1-0">a</a> <a href="#cite_ref-ReferenceA_1-1">b</a> Smith, Warren Modern Optical Engineering, 4th Ed., 2007 McGraw-Hill Professional, p. 183. </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFHecht1987" class="citation book cs1">Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. p. 152. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-11609-X" title="Special:BookSources/0-201-11609-X"><bdi>0-201-11609-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics&rft.pages=152&rft.edition=2nd&rft.pub=Addison+Wesley&rft.date=1987&rft.isbn=0-201-11609-X&rft.aulast=Hecht&rft.aufirst=Eugene&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreivenkamp2004" class="citation book cs1">Greivenkamp, John E. (2004). Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. Bellingham, Wash: <a href="/wiki/SPIE#SPIE_Press" title="SPIE">SPIE</a>. p. 29. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780819452948" title="Special:BookSources/9780819452948"><bdi>9780819452948</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/53896720">53896720</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Field+Guide+to+Geometrical+Optics&rft.place=Bellingham%2C+Wash&rft.series=SPIE+Field+Guides+vol.+FG01&rft.pages=29&rft.pub=SPIE&rft.date=2004&rft_id=info%3Aoclcnum%2F53896720&rft.isbn=9780819452948&rft.aulast=Greivenkamp&rft.aufirst=John+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> Smith, Warren Modern Lens Design 2005 McGraw-Hill. </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> ISO, Photography—Apertures and related properties pertaining to photographic lenses—Designations and measurements, ISO 517:2008 </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> See <a href="/wiki/Area_of_a_circle" title="Area of a circle">Area of a circle</a>. </li> <li id="cite_note-7"><a href="#cite_ref-7">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarry_C._Box2003" class="citation book cs1">Harry C. Box (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=YjAzP4i1oFcC&pg=PA136">Set lighting technician's handbook: film lighting equipment, practice, and electrical distribution</a> (3rd ed.). Focal Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-240-80495-8" title="Special:BookSources/978-0-240-80495-8"><bdi>978-0-240-80495-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Set+lighting+technician%27s+handbook%3A+film+lighting+equipment%2C+practice%2C+and+electrical+distribution&rft.edition=3rd&rft.pub=Focal+Press&rft.date=2003&rft.isbn=978-0-240-80495-8&rft.au=Harry+C.+Box&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DYjAzP4i1oFcC%26pg%3DPA136&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-8"><a href="#cite_ref-8">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPaul_Kay2003" class="citation book cs1">Paul Kay (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DvYMl-s1_9YC&pg=PA19">Underwater photography</a>. Guild of Master Craftsman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-86108-322-7" title="Special:BookSources/978-1-86108-322-7"><bdi>978-1-86108-322-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Underwater+photography&rft.pub=Guild+of+Master+Craftsman&rft.date=2003&rft.isbn=978-1-86108-322-7&rft.au=Paul+Kay&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DDvYMl-s1_9YC%26pg%3DPA19&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_W._Samuelson1998" class="citation book cs1">David W. Samuelson (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=IWkpoJKM_ucC&pg=PA145">Manual for cinematographers</a> (2nd ed.). Focal Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-240-51480-2" title="Special:BookSources/978-0-240-51480-2"><bdi>978-0-240-51480-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Manual+for+cinematographers&rft.edition=2nd&rft.pub=Focal+Press&rft.date=1998&rft.isbn=978-0-240-51480-2&rft.au=David+W.+Samuelson&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DIWkpoJKM_ucC%26pg%3DPA145&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-10"><a href="#cite_ref-10">^</a> <a rel="nofollow" class="external text" href="https://www.dxomark.com/glossary/transmission-light-transmission/">Transmission, light transmission</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210508111318/https://www.dxomark.com/glossary/transmission-light-transmission/">Archived</a> 2021-05-08 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, DxOMark </li> <li id="cite_note-11"><a href="#cite_ref-11">^</a> <a rel="nofollow" class="external text" href="https://www.dxomark.com/sigma-85mm-f1-4-art-lens-review-new-benchmark/">Sigma 85mm F1.4 Art lens review: New benchmark</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180104073126/https://www.dxomark.com/sigma-85mm-f1-4-art-lens-review-new-benchmark/">Archived</a> 2018-01-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, DxOMark </li> <li id="cite_note-12"><a href="#cite_ref-12">^</a> <a rel="nofollow" class="external text" href="https://www.lenstip.com/129.1-article-Colour_rendering_in_binoculars_and_lenses.html">Colour rendering in binoculars and lenses - Colours and transmission</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180104013937/https://www.lenstip.com/129.1-article-Colour_rendering_in_binoculars_and_lenses.html">Archived</a> 2018-01-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, LensTip.com </li> <li id="cite_note-KMPCF-13">^ <a href="#cite_ref-KMPCF_13-0">a</a> <a href="#cite_ref-KMPCF_13-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20021002095739/http://www.kodak.com/US/en/motion/support/h2/intro01P.shtml">"Kodak Motion Picture Camera Films"</a>. <a href="/wiki/Eastman_Kodak" class="mw-redirect" title="Eastman Kodak">Eastman Kodak</a>. November 2000. Archived from <a rel="nofollow" class="external text" href="http://www.kodak.com/US/en/motion/support/h2/intro01P.shtml">the original</a> on 2002-10-02. Retrieved 2007-09-02.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Kodak+Motion+Picture+Camera+Films&rft.pub=Eastman+Kodak&rft.date=2000-11&rft_id=http%3A%2F%2Fwww.kodak.com%2FUS%2Fen%2Fmotion%2Fsupport%2Fh2%2Fintro01P.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://forums.dpreview.com/forums/post/33785655">"Marianne Oelund, "Lens T-stops", dpreview.com, 2009"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121110221724/http://forums.dpreview.com/forums/post/33785655">Archived</a> from the original on 2012-11-10. Retrieved 2013-01-11.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Marianne+Oelund%2C+%22Lens+T-stops%22%2C+dpreview.com%2C+2009&rft_id=http%3A%2F%2Fforums.dpreview.com%2Fforums%2Fpost%2F33785655&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-15"><a href="#cite_ref-15">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichael_John_Langford2000" class="citation book cs1">Michael John Langford (2000). <a rel="nofollow" class="external text" href="https://archive.org/details/basicphotography00lang">Basic Photography</a>. <a href="/wiki/Focal_Press" title="Focal Press">Focal Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-240-51592-7" title="Special:BookSources/0-240-51592-7"><bdi>0-240-51592-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Basic+Photography&rft.pub=Focal+Press&rft.date=2000&rft.isbn=0-240-51592-7&rft.au=Michael+John+Langford&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbasicphotography00lang&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-16"><a href="#cite_ref-16">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLevy2001" class="citation book cs1">Levy, Michael (2001). Selecting and Using Classic Cameras: A User's Guide to Evaluating Features, Condition & Usability of Classic Cameras. Amherst Media, Inc. p. 163. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-58428-054-5" title="Special:BookSources/978-1-58428-054-5"><bdi>978-1-58428-054-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Selecting+and+Using+Classic+Cameras%3A+A+User%27s+Guide+to+Evaluating+Features%2C+Condition+%26+Usability+of+Classic+Cameras&rft.pages=163&rft.pub=Amherst+Media%2C+Inc&rft.date=2001&rft.isbn=978-1-58428-054-5&rft.aulast=Levy&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-17"><a href="#cite_ref-17">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHecht1987" class="citation book cs1">Hecht, Eugene (1987). Optics (2nd ed.). <a href="/wiki/Addison_Wesley" class="mw-redirect" title="Addison Wesley">Addison Wesley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-11609-X" title="Special:BookSources/0-201-11609-X"><bdi>0-201-11609-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics&rft.edition=2nd&rft.pub=Addison+Wesley&rft.date=1987&rft.isbn=0-201-11609-X&rft.aulast=Hecht&rft.aufirst=Eugene&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> Sect. 5.7.1 </li> <li id="cite_note-RefDesign-18"><a href="#cite_ref-RefDesign_18-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCharles_F._Claver2007" class="citation journal cs1">Charles F. Claver; et al. (2007-03-19). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090306173830/http://lsst.org/files/docs/LSST-RefDesign.pdf">"LSST Reference Design"</a> (PDF). LSST Corporation: 45–50. Archived from <a rel="nofollow" class="external text" href="http://lsst.org/files/docs/LSST-RefDesign.pdf">the original</a> (PDF) on 2009-03-06. Retrieved 2011-01-10.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=LSST+Reference+Design&rft.pages=45-50&rft.date=2007-03-19&rft.au=Charles+F.+Claver&rft_id=http%3A%2F%2Flsst.org%2Ffiles%2Fdocs%2FLSST-RefDesign.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> <code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: Cite journal requires <code class="cs1-code">|journal=</code> (<a href="/wiki/Help:CS1_errors#missing_periodical" title="Help:CS1 errors">help</a>) </li> <li id="cite_note-g-number-19"><a href="#cite_ref-g-number_19-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDriggers2003" class="citation book cs1">Driggers, Ronald G. (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rcrGlrguj1YC">Encyclopedia of Optical Engineering: Pho-Z, pages 2049-3050</a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8247-4252-2" title="Special:BookSources/978-0-8247-4252-2"><bdi>978-0-8247-4252-2</bdi></a>. Retrieved 2020-06-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Encyclopedia+of+Optical+Engineering%3A+Pho-Z%2C+pages+2049-3050&rft.pub=CRC+Press&rft.date=2003&rft.isbn=978-0-8247-4252-2&rft.aulast=Driggers&rft.aufirst=Ronald+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DrcrGlrguj1YC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-Greivenkamp-20">^ <a href="#cite_ref-Greivenkamp_20-0">a</a> <a href="#cite_ref-Greivenkamp_20-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreivenkamp2004" class="citation book cs1">Greivenkamp, John E. (2004). Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. SPIE. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8194-5294-7" title="Special:BookSources/0-8194-5294-7"><bdi>0-8194-5294-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Field+Guide+to+Geometrical+Optics&rft.pub=SPIE&rft.date=2004&rft.isbn=0-8194-5294-7&rft.aulast=Greivenkamp&rft.aufirst=John+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> p. 29. </li> <li id="cite_note-Sutton-21"><a href="#cite_ref-Sutton_21-0">^</a> Thomas Sutton and George Dawson, A Dictionary of Photography, London: Sampson Low, Son & Marston, 1867, (p. 122). </li> <li id="cite_note-Dallmeyer-22">^ <a href="#cite_ref-Dallmeyer_22-0">a</a> <a href="#cite_ref-Dallmeyer_22-1">b</a> John Henry Dallmeyer, Photographic Lenses: On Their Choice and Use – Special Edition Edited for American Photographers, pamphlet, 1874. </li> <li id="cite_note-23"><a href="#cite_ref-23">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSouthall1910" class="citation book cs1">Southall, James P. 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Macmillan. p. 537.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Principles+and+Methods+of+Geometrical+Optics%3A+Especially+as+applied+to+the+theory+of+optical+instruments&rft.pages=537&rft.pub=Macmillan&rft.date=1910&rft.aulast=Southall&rft.aufirst=James+P.+C.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fprinciplesandme01soutgoog%2Fpage%2Fn493&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-Czapski-24">^ <a href="#cite_ref-Czapski_24-0">a</a> <a href="#cite_ref-Czapski_24-1">b</a> Siegfried Czapski, Theorie der optischen Instrumente, nach Abbe, Breslau: Trewendt, 1893. </li> <li id="cite_note-25"><a href="#cite_ref-25">^</a> Henry Crew, "Theory of Optical Instruments by Dr. Czapski," in Astronomy and Astro-physics XIII pp. 241–243, 1894. </li> <li id="cite_note-26"><a href="#cite_ref-26">^</a> Thomas R. Dallmeyer, Telephotography: An elementary treatise on the construction and application of the telephotographic lens, London: Heinemann, 1899. </li> <li id="cite_note-27"><a href="#cite_ref-27">^</a> C. H. Bothamley, Ilford Manual of Photography, London: Britannia Works Co. Ltd., 1891. </li> <li id="cite_note-28"><a href="#cite_ref-28">^</a> John A. Hodges, Photographic Lenses: How to Choose, and How to Use, Bradford: Percy Lund & Co., 1895. </li> <li id="cite_note-29"><a href="#cite_ref-29">^</a> C. Welborne Piper, A First Book of the Lens: An Elementary Treatise on the Action and Use of the Photographic Lens, London: Hazell, Watson, and Viney, Ltd., 1901. </li> <li id="cite_note-30"><a href="#cite_ref-30">^</a> Conrad Beck and Herbert Andrews, Photographic Lenses: A Simple Treatise, second edition, London: R. & J. Beck Ltd., c. 1902. </li> <li id="cite_note-31"><a href="#cite_ref-31">^</a> <a rel="nofollow" class="external text" href="https://books.google.com/books?as_q=lens+aperture&num=50&as_epq=f-number">Google search</a> </li> <li id="cite_note-32"><a href="#cite_ref-32">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIves1920" class="citation book cs1">Ives, Herbert Eugene (1920). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ypakouuKvwYC&pg=RA2-PA61">Airplane Photography</a> (Google). Philadelphia: J. B. Lippincott. p. 61. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780598722225" title="Special:BookSources/9780598722225"><bdi>9780598722225</bdi></a>. Retrieved 2007-03-12.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Airplane+Photography&rft.place=Philadelphia&rft.pages=61&rft.pub=J.+B.+Lippincott&rft.date=1920&rft.isbn=9780598722225&rft.aulast=Ives&rft.aufirst=Herbert+Eugene&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DypakouuKvwYC%26pg%3DRA2-PA61&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-33"><a href="#cite_ref-33">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMees1920" class="citation book cs1">Mees, Charles Edward Kenneth (1920). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=V7MCVGREPfkC&q=aperture+lens+uniform-system+date:0-1930">The Fundamentals of Photography</a>. Eastman Kodak. p. 28. Retrieved 2007-03-12.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fundamentals+of+Photography&rft.pages=28&rft.pub=Eastman+Kodak&rft.date=1920&rft.aulast=Mees&rft.aufirst=Charles+Edward+Kenneth&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DV7MCVGREPfkC%26q%3Daperture%2Blens%2Buniform-system%2Bdate%3A0-1930&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> <li id="cite_note-34"><a href="#cite_ref-34">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDerr1906" class="citation book cs1">Derr, Louis (1906). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=AN6d4zTjquwC&pg=PA83">Photography for Students of Physics and Chemistry</a> (Google). London: Macmillan. p. 83. Retrieved 2007-03-12.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Photography+for+Students+of+Physics+and+Chemistry&rft.place=London&rft.pages=83&rft.pub=Macmillan&rft.date=1906&rft.aulast=Derr&rft.aufirst=Louis&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DAN6d4zTjquwC%26pg%3DPA83&rfr_id=info%3Asid%2Fen.wikipedia.org%3AF-number" class="Z3988"> </li> </ol></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(11)"><h2 id="External_links">External links</h2> <a role="button" href="/w/index.php?title=F-number&action=edit&section=24" title="Edit section: External links" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-11 collapsible-block" id="mf-section-11"> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output 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href="/w/index.php?title=F-number&action=history"> <div class="post-content last-modified-bar__content"> Last edited on 3 November 2024, at 15:01 </div> </a> <div class="post-content footer-content"> <div id='mw-data-after-content'> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Languages</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/F-nommer" title="F-nommer – Afrikaans" lang="af" hreflang="af" data-title="F-nommer" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%A7%D9%84%D8%A8%D8%A4%D8%B1%D8%A9" title="عدد البؤرة – Arabic" lang="ar" hreflang="ar" data-title="عدد البؤرة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%8F%E0%A6%AB-%E0%A6%A8%E0%A6%BE%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A6%BE%E0%A6%B0" title="এফ-নাম্বার – Bangla" lang="bn" hreflang="bn" data-title="এফ-নাম্বার" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9B%D1%96%D0%BA_%D0%B4%D1%8B%D1%8F%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D1%8B" title="Лік дыяфрагмы – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Лік дыяфрагмы" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D0%BD%D0%B0_%D0%B0%D0%BF%D0%B5%D1%80%D1%82%D1%83%D1%80%D0%B0" title="Относителна апертура – Bulgarian" lang="bg" hreflang="bg" data-title="Относителна апертура" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_f" title="Nombre f – Catalan" lang="ca" hreflang="ca" data-title="Nombre f" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Clonov%C3%A9_%C4%8D%C3%ADslo" title="Clonové číslo – Czech" lang="cs" hreflang="cs" data-title="Clonové číslo" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Blendenzahl" title="Blendenzahl – German" lang="de" hreflang="de" data-title="Blendenzahl" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82_%CE%B4%CE%B9%CE%B1%CF%86%CF%81%CE%AC%CE%B3%CE%BC%CE%B1%CF%84%CE%BF%CF%82_%CE%B1%CE%BD%CE%BF%CE%AF%CE%B3%CE%BC%CE%B1%CF%84%CE%BF%CF%82" title="Αριθμός διαφράγματος ανοίγματος – Greek" lang="el" hreflang="el" data-title="Αριθμός διαφράγματος ανοίγματος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_f_(%C3%B3ptica)" title="Número f (óptica) – Spanish" lang="es" hreflang="es" data-title="Número f (óptica)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Relativa_truo_de_objektivo" title="Relativa truo de objektivo – Esperanto" lang="eo" hreflang="eo" data-title="Relativa truo de objektivo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/F_zenbakia_(optika)" title="F zenbakia (optika) – Basque" lang="eu" hreflang="eu" data-title="F zenbakia (optika)" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B6%D8%B1%DB%8C%D8%A8_%D8%A7%D9%81" title="ضریب اف – Persian" lang="fa" hreflang="fa" data-title="ضریب اف" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ouverture_(photographie)" title="Ouverture (photographie) – French" lang="fr" hreflang="fr" data-title="Ouverture (photographie)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/F-uimhir" title="F-uimhir – Irish" lang="ga" hreflang="ga" data-title="F-uimhir" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/F_%EA%B0%92" title="F 값 – Korean" lang="ko" hreflang="ko" data-title="F 값" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D6%80%D5%A1%D5%A2%D5%A5%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A1%D5%B6%D6%81%D6%84" title="Հարաբերական անցք – Armenian" lang="hy" hreflang="hy" data-title="Հարաբերական անցք" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AB%E0%A5%8B%E0%A4%95%E0%A4%B8_%E0%A4%85%E0%A4%A8%E0%A5%81%E0%A4%AA%E0%A4%BE%E0%A4%A4" title="फोकस अनुपात – Hindi" lang="hi" hreflang="hi" data-title="फोकस अनुपात" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bukaan_(fotografi)" title="Bukaan (fotografi) – Indonesian" lang="id" hreflang="id" data-title="Bukaan (fotografi)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Lj%C3%B3sop" title="Ljósop – Icelandic" lang="is" hreflang="is" data-title="Ljósop" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rapporto_focale" title="Rapporto focale – Italian" lang="it" hreflang="it" data-title="Rapporto focale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%99%D7%97%D7%A1_%D7%9E%D7%99%D7%A7%D7%95%D7%93" title="יחס מיקוד – Hebrew" lang="he" hreflang="he" data-title="יחס מיקוד" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/F_skai%C4%8Dius" title="F skaičius – Lithuanian" lang="lt" hreflang="lt" data-title="F skaičius" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%8E%E0%B4%AB%E0%B5%8D%E2%80%8C-%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="എഫ്‌-സംഖ്യ – Malayalam" lang="ml" hreflang="ml" data-title="എഫ്‌-സംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Nombor_f_(fotografi)" title="Nombor f (fotografi) – Malay" lang="ms" hreflang="ms" data-title="Nombor f (fotografi)" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Diafragmagetal" title="Diafragmagetal – Dutch" lang="nl" hreflang="nl" data-title="Diafragmagetal" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/F%E5%80%A4" title="F値 – Japanese" lang="ja" hreflang="ja" data-title="F値" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D0%BE%D1%82%D0%B2%D0%B5%D1%80%D1%81%D1%82%D0%B8%D0%B5" title="Относительное отверстие – Russian" lang="ru" hreflang="ru" data-title="Относительное отверстие" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Clonov%C3%A9_%C4%8D%C3%ADslo" title="Clonové číslo – Slovak" lang="sk" hreflang="sk" data-title="Clonové číslo" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Aukkosuhde" title="Aukkosuhde – Finnish" lang="fi" hreflang="fi" data-title="Aukkosuhde" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%81%E0%AE%B5%E0%AE%BF%E0%AE%AF_%E0%AE%B5%E0%AE%BF%E0%AE%95%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="குவிய விகிதம் – Tamil" lang="ta" hreflang="ta" data-title="குவிய விகிதம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B9%88%E0%B8%B2%E0%B9%80%E0%B8%AD%E0%B8%9F" title="ค่าเอฟ – Thai" lang="th" hreflang="th" data-title="ค่าเอฟ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/F-stop" title="F-stop – Turkish" lang="tr" hreflang="tr" data-title="F-stop" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D1%96%D0%B0%D1%84%D1%80%D0%B0%D0%B3%D0%BC%D0%BE%D0%B2%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Діафрагмове число – Ukrainian" lang="uk" hreflang="uk" data-title="Діафрагмове число" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%84%A6%E6%AF%94" title="焦比 – Chinese" lang="zh" hreflang="zh" data-title="焦比" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li></ul> </section> </div> <div class="minerva-footer-logo"><img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 1.125em;"/> </div> <ul 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