# Aperture formula

My camera is Fujifilm s7000 (bridge) . On the lens I can see f = 7.8mm - 46.8mm . When using the formula should we use 35mm equivalents values ? Does optical zooming change the focal length?

aperture = F / x

x = 2.8 , 4 , 22 etc

• Are you being confused because there's two things called "f"? Little `f` is the focal length and big `F` is the aperture. – Mark Ransom Jan 25 '18 at 21:50
• Sorry , the formula is Focal Length/f ? e.g 200mm/2.8 that is what I mean . Where I confused is in the manual it has give actual and 35 equivalent mm . So to use in the formula should I need to actual mm or 35 equivalent mm ? – nish1013 Jan 25 '18 at 21:59
• Could you try and explain the actual photographic problem you're trying to solve here? Calculating numbers is all well and good, but it's not photography. – Philip Kendall Jan 25 '18 at 22:05
• I want get the shortest depth of field from my camera. I tried with Apeature priority mode. 1) no zoom f/2.8 2) max zoom f/3.1. . The option 2 gave me the desired result. So I think this is due to widest opening i.e 46.8mm / 3.1 ? – nish1013 Jan 25 '18 at 22:14

I want get the shortest depth of field from my camera.

The slimmest Depth of Field (DOF) will be at the minimum focusing distance of the most telephoto end using the largest aperture (largest as in physical opening).

Using a DOF calculator, I found the DOF to be 0.6 inches when focusing at 3 ft using f/3.2 at 46.8mm. (minimum focusing distance, largest aperture, zoomed all the way)

Contrast this with the DOF at the wide end, which is 6.2 inches focusing at 1.6 ft using f/2.8 at 7.8mm.

• It's unusual for the minimum F-stop to be so close at both ends of the zoom range. Even so, the shallowest DOF is usually at the long end. – Mark Ransom Jan 25 '18 at 23:51
• @MarkRansom, I'm confused by your comment. How is it unusual that the minimum f-stop is close together? We have plenty of zoom options that hold f/2.8 all the way through, for example. The specs that I used for the example come from the S7000 manual (max aperture, minimum focusing distance, focal length) – Hueco Jan 26 '18 at 0:28
• It's unusual for a 6x zoom range, most constant aperture zooms are well below that. And I wasn't questioning your answer at all, just leaving a turd for future visitors with different cameras. You have my +1. – Mark Ransom Jan 26 '18 at 1:03
• @MarkRansom - I took no offense. Just trying to clarify :-). I'm just getting into optics...I wonder if the small sensor size had some benefit in keeping the aperture from losing more stops? – Hueco Jan 26 '18 at 1:25
• The more of the increased magnification between the shortest and longest FL that is in front of the physical diaphragm, the more constant the aperture will remain. Any magnification that occurs behind the physical diaphragm as the lens is zoomed will not also magnify the entrance pupil and the f-number will go up. – Michael C Jan 26 '18 at 3:16

You appear to want to calculate the DOF of your camera. The formulas that do this require the actual focal length, not the 35mm equivalent.

The DOF formulas will take both focal length and F-stop into account. In general a longer focal length will give a shorter DOF, but most lenses will have a larger minimum F-stop as they get longer too; the two factors will cancel each other to a degree.

Smaller sensor cameras generally give you larger DOF than large sensor ones, but it becomes harder to get a totally blurred background.

• You also need the actual sensor size so that the magnification between the size of the sensor and the desired display size can also be taken into account. – Michael C Jan 26 '18 at 3:17
• @MichaelClark I thought the sensor size mattered only indirectly, by affecting the number you use for CoC? – Mark Ransom Jan 26 '18 at 3:59
• CoC is determined by the magnification of a specific sensor size to the specified display size. It's the largest size blur circle we perceive as a single point. If the display size is not specified, it is assumed to be 8x10 inches viewed from 10-12 inches. CoC can also be affected by the assumption regarding the viewers' visual acuity. Most camera manufacturers used 20/20. Zeiss used 20/15. – Michael C Jan 26 '18 at 6:27
• Please see this answer for more. – Michael C Jan 26 '18 at 6:33

Optical zooming does change the focal length, yes. It changes in the denoted range. The 35 mm equivalent is included just to give an idea of what the angle of view will be (because many people are used to dealing in 35 mm terms); it is also used as a selling point. The aperture opening you have will be 7.8/2.8≈2.786 mm at the wide end and 46.8/3.1≈15.097 mm at the tele end. The aperture value is given using an f-number because this is directly related to the light gathering abilities of the lens and because otherwise (if you give the absolute value), you also have to include the focal length for it to make sense.

• So in my camera I get highest apearture when at 46.8mm . To get to 46.8mm I have to use max zoom . Am I correct? – nish1013 Jan 25 '18 at 21:55
• Be very careful using a term like "highest aperture" - an aperture with a larger number (e.g. f/5.6) means a narrower opening and therefore less light than an aperture with a smaller number (e.g. f/2.8). Your camera is perfectly capable of using a narrower aperture (e.g. f/5.6) at the wide-angle end of the lens, but is not capable of using a wider aperture (e.g. f/2.8) at the telephoto end of the lens. In most cases on a compact camera, you want as wide an aperture as possible, so f/2.8 is better than f/3.1 or f/5.6. – Philip Kendall Jan 25 '18 at 22:02
• The actual physical size of the aperture opening does not change. The entrance pupil size changes because the magnification between the front of the lens and the physical diaphragm changes. – Michael C Jan 26 '18 at 3:19