# Do f-stops scale with sensor size the way focal length does? [duplicate]

Does the aperture rating scale with sensor size the way focal length does?

For example, is a 25mm 1.2 MFT lens equivalent to a 50mm 1.2 FF lens or to a 50mm 2.0 FF lens?

• Also related (given your answer to your own question): Is crop-factor a bad thing? Jul 23 '17 at 21:33
• you scale the length and the appropriate ratio, 25/1.2 is equivalent to 50/2.4, which determines the light gathering working diameter of the aperture in mm, so 20mm working aperture FF equivalent whether its on 25 or a 50, but the 50mm depicts the angle of view Jan 19 '19 at 9:57
• There's no such thing as true equivalence when using different sensor sizes to try and take the same picture. To preserve some variables, other variables must change. If we use the same shooting distance (to have the same perspective), a different focal length (to have the same angle-of-view), and the same ISO and exposure time (so that any motion is recorded the same), then using the same aperture gives the same exposure but different depth-of-field. Using a different aperture to get the same DoF results in different exposure. Jan 7 '20 at 19:25

No, f/stop does not vary with sensor size.

Nor does focal length vary with sensor size. The lens remains totally unaffected by the sensor.

HOWEVER, the field of view that the cropped sensor can see and capture is seriously affected in the smaller sensor. We might imagine that to be a lens difference, but it is only a sensor difference.

Exposure does "vary" with lens focal length, therefore the whole idea of inventing f/stop numbering is that f/stop does not vary.

f/stop = focal length / aperture diameter.

A lens twice longer has an aperture of twice diameter, for same f/stop number, and same exposure.

So regardless of the "size of the lens" (diameter or focal length), the same computed f/stop number represents the same exposure.

This is complicated slightly in that each glass-air surface in the lens has slight transmission losses, which is greater in lenses with more glass elements. However, modern lens coatings reduce this loss to a small factor, easily negligible in still photo cameras.

For example, is a 25mm 1.2 MFT lens equivalent to a 50mm 1.2 FF lens or to a 50mm 2.0 FF lens?

In terms of exposure a 25mm f/1.2 Micro Four-Thirds lens is equivalent to a 50mm f/1.2 lens used on a full frame camera.

In terms of the resulting depth of field the 25mm f/1.2 Micro Four-Thirds lens is equivalent to a 50mm f/2.5 (2-stop difference)¹ lens used on a full frame camera if the camera-subject distance used is the same and the results from both cameras are viewed at the same display size.

There is no such thing as full equivalency between different photographic formats.

¹ Technically, a Micro Four-Thirds lens with an exact aperture of f/1.2 would be equivalent to an f/2.4 lens when used on a FF camera. But f/1.2 is really either f/1.189 when using a half-stop scale or f/1.26 when using a one-third stop scale. F/1.189 is exactly halfway between F/1 and f/√2 (which we refer to as f/1.4). f/1.26 is two-thirds of the way between f/1 and f/√2 (f/1.4). Since most of us these days use one-third stop aperture scales, two stops from f/1.26 is f/2.52, which we express as f/2.5. If one is using a half-stop scale, two stops from f/1.189 is f/2.378, which we express as f/2.4.

The f-number system aids photographers enabling them to adjust their cameras so that the exposing light energy delivers an optimal exposure. Now the lens mimics a funnel in that it gathers light. The greater the working diameter of the lens, the greater is its light gathering power. That’s only half the story. The greater the focal length, the dimmer will be the image projected by the lens. In other words, image brightness is intertwined with working diameter and focal length.

Ratio to the rescue: We divide the focal length by the working diameter to obtain the focal ratio. As a example, it the lens has a focal length of 100mm and a working diameter of 25mm, then the focal ratio is 100 ÷ 25 = 4 written as f/4. Same is true if the lens focal length 1000mm focal length with a working diameter of 250mm. Both operate at f/4 – both deliver the same light energy during the exposure.

The bottom line is the focal ratio or f-number is a universal value that we can use to set the working diameter. Any lens set to the same f-number delivers the same image brilliance regardless of its diameter or focal length.

The bottom line is : f-numbers are universal and independent of format size.

Not really. F number is defined as ratio of focal length and entrance pupil. Nothing about sensor size here.

But - there is always a but - you will find that lens designed for larger formats tend to have higher f numbers. Medium format film lens have higher f stops than 35mm lenses and large format lens even bigger.

The reason is that it is impractical to manufacture (or carry around) a lens with a really big entrance pupil i.e. front element.

Aperture numbers are detached from focal length and sensor size. They basically tell how much of the light arriving from a scene will arrive in the image plane after being sorted by the lens. If you don't use a lens at all, the overall brightness corresponds to f:1, so an f:1.2 lens does not lose a lot of brightness compared to a big hole even though it does a much better job at sorting light arriving from different directions into an image.

So how do crop factors and focal length come into play? The crop factor tells how large the served image area actually is. The aperture number is only valid within that image circle. The larger the image circle is, the more light needs to be collected to serve it at equal brightness and thus equal aperture number. Collecting light from a larger entrance pupil means that sorting the light according to the direction it arrives in makes the image more susceptible to how near objects are to the focus plane. So as the crop factor gets smaller and the image/sensor area becomes larger, so does the entrance pupil and the depth of focus decreases.

So what's with focal length? Focal length determines the scale at which objects get depicted. Larger focal length for an idealised single-element lens means placing a weaker element at a larger distance to the image plane, resulting in a larger image. Scaling up the image does not magically make for more light, so we need to capture more light to make up for it. So that's the reason the entrance pupil has a diameter of focal length divided by aperture number.

And effective focal length? The image has a size, a framing. If the lens creates a large image and we only take a small part of it, the result looks as though we had worked with a larger focal length.

So a 25mm/1.2 MFT lens produces the framing and overall light yield of a 50mm/1.2 full-frame lens. However, this light yield only fills a quarter of your image area and thus can be collected from a quarter of the entrance pupil. Consequently the depth of field corresponds to that of a 50mm/2.4 full-frame lens.

So what you call "equivalent" in aperture depends on whether you are looking at the resulting light yield or the resulting depth of field.

I did some more research to answer this question for myself.

The MFT apertures are equivalent to the FF in terms of brightness, so a 25mm 1.2 MFT lens is equivalent to a 50mm 1.2 FF in that using the same ISO setting on both will produce images of equal field of view and brightness (assuming that sensor is the same quality). Note that some of the latest MFT sensors have low noise improvements that make them about half a stop brighter than all but the latest and most expensive FF cameras.

The main difference, other than field of view, is depth of field. The MFTs have a deeper focus range and you have to go about 2 stops tighter in a FF to get the same depth of field as an MFT. So, if you are taking table top photos and want the whole object to be in focus, then MFT will be better, but if you are taking portraits and want just the subject to be in focus and everything else to be blurred ("separation"), then FF will be better.

• This does not answer the question.
– user50888
Jul 23 '17 at 21:01
• This is roughly correct. The part about "latest MFT sensors" being "half a stop brighter" is off, though. Even assuming that the MFT sensors have a noise advantage (which may happen to be true at this point in time; I don't follow the ups and downs of that since narrow edges in tech change rapidly), that doesn't mean that the images will be brighter. Jul 23 '17 at 21:31
• Assuming you mean that the latest MFT cameras have a half-stop noise advantage vs. current technology sensors in other cameras, I'm not convinced. See this studio seen comparison at ISO 3200. Jul 23 '17 at 21:42
• That's the latest Olympus flagship next to some recent lower-level APS-C cameras. To my eye, the Olympus is a little bit better than the Canon example, and comparable to or a little bit worse than the other cameras with recent made-by-Sony sensors. If you put in full-frame cameras like the Pentax K-1, there's a clear noise advantage even down to lower ISOs. Jul 23 '17 at 21:48
• @TylerDurden No, please read what I just read and read the links if you don't believe me. These comparisons are with APS-C sensors in current models. Jul 23 '17 at 22:09