Why does crop factor apply with APS-C lenses, and why aren't these brighter than FF ones at same aperture?

Question

I know that the image circle of FF-lenses is bigger than it needs to be on APS-C sensors, thus the FOV spears narrower. I've heard that APS-C lenses sit closer to the sensor, thus projecting a smaller image circle around it. To this, I have two questions:

1. Why does crop factor apply with APS-C-lenses, while it sounds like the image circle is compressed onto the APS-C-sensor (thus making a wider FOV)?

2. Because of the assumed light-compression, why aren't APS-C-lenses brighter on APS-C-sensors than FF-lenses at the same apertures?

I assume there is one answer to both questions. I have asked my friend google, but he couldn't come up with an explanation.

Answer 1

Your logic is sound. If your assumptions were right, then your conclusion would be right.

Let me turn one of your questions around. You ask:

Why does crop factor apply with APS-C-lenses, while it sounds like the image circle is compressed onto the APS-C-sensor (thus making a wider FOV)?

In fact, the image circle isn't compressed, and does not make a wider FOV. It just doesn't extend as far outside of the frame as the circle projected by a lens designed for a larger format would. So the first part is naturally true: the actual projected image within that circle is the same for any focal length, and so if you take less of it, you're cropping — or, "the crop factor applies".

Because of the assumed light-compression, why aren't APS-C-lenses brighter on APS-C-sensors than FF-lenses at the same apertures?

Again, because there isn't any. So, remove that bad assumption and replace it with "the image circle is a design parameter not directly related to sensor size". To quote again:

I know that the image circle of FF-lenses is bigger than it needs to be on APS-C sensors, thus the FOV appears narrower.

This is not true. The FOV appears narrower only because the smaller sensor picks up less of the image circle, regardless of how big that image circle is. There's more on this at Do the same camera settings lead to the same exposure across different sensor sizes?.

However, there are lenses adapters that do work basically this way: "speedboosters" (see How can a speedbooster improve the light performance of a lens?). These do "compress the light" to a smaller circle. But note that by doing so, they also change the focal length. When you calculate the exposure per area of the result, taking into account the new focal length and the new effective aperture, it will be no different from a full-frame (or large-format!) lens of that same effective aperture.

Answer 2

The image circle produced by a lens is independent of the focal length. It is the combination of the focal length and the sensor size that determine the effective FOV. For example, a 90mm lens designed for a view camera with film that is 4x5 inches in size will have a wide angle FOV on that camera. But take that same lens and mount it on a DSLR with an APS-C sensor and the lens/sensor combination will produce a narrow FOV. You can imagine taking taking a piece of paper with an APS-C sensor sized cutout and placing it over the 4x5 negative. That's essentially what's happening with cameras with different sensor sizes (although the lenses themselves can be designed with smaller image circles if the sensor sizes are smaller, which can make the design of the lenses simpler or weigh less).

The same thing is happening with DSLRs between FF and APS-C, you can mount the same 50mm lens on a FF and APS-C camera -- where the only difference is the size of the sensor -- and the APS-C camera's FOV will be more narrow than the FF camera.

A lens' f stop is also independent of the sensor size (ideally ... there is some light falloff on the edges). This is an imperfect analogy, but imagine shining a light on a small piece of paper. If you cut the paper in half, would the intensity of the light be doubled?

If the lens was designed to have a higher light transmission, it would also have different f stops. If the lens was designed to sit closer to the camera it would have a lower focal length (generally).

Answer 3

You are misunderstanding a few things that are causing you confusion. The only difference between a lens designed for a full frame sensor and a lens designed for an APS-c sensor is that the APS-c lens collects less light since it is producing a smaller image circle. The light per surface area of the image circle is the same, but the circle is smaller. An APS-c lens does not necessarily sit closer to the sensor, in fact, for the same lens, an APS-c sensor and a full frame sensor will be exactly the same distance away, though some APS-c lenses make use of the smaller mirror to allow themselves to extend further in to the camera.

Further, focal length, which is how lenses are broadly categorized, has nothing to do with crop factor. There is no compression of an APS-c image on to the sensor. An APS-c lens will crop the image circle itself and the reason that crop-factor occurs is because the sensor only covers a portion of a full frame image circle. With a full frame lens, light would be focused off the edges of the sensor as more light is gathered than is needed. In an APS-c lens of the same focal length, the amount of magnification at a given distance is the same, however it only gathers and projects the light needed for covering the sensor. If you were to put a 35mm APS-c lens on an APS-c camera and look at the image on the sensor, it would be exactly the same as if you put a full frame lens, but the full frame lens would have an image circle bigger than the sensor.

The fact that there is no compression of the light is also why it isn't brighter. The APS-c lens simply gathers less light to begin with. This is why it is said that FF cameras have an advantage in low light, because the full frame lens pulls in more light than the APS-c lens and the FF sensor is able to make use of all of it.

Answer 4

While the question has actually already been well answered, I just wanted to mention the term flange focal distance (also called flange to film distance), see e.g. Wikipedia. Basically, the camera manufacturers as Nikon and Canon have developed their first DSLR's using image sensors smaller than the illuminated film area of 135 film. As they did not want to completely develop new lenses, they continued to use the same flange focal distance, being the distance between film / digital sensor and the flange of the camera bayonet. Therefore, if a FF lens (with a larger imaging circle compared to a lens for cropped sensors) is mounted on a cropped sensor camera, the light of the larger imaging circle is "lost".