Brightness of a full frame lens mounted on aps-c vs mounting an identical native aps-c lens [duplicate]

Question

I am a bit confused about the effect of using a full-frame lens on a aps-c camera on the brightness of the resulting image.

Lets say we have two lenses:

• A full frame 50mm f2 lens
• An aps-c 50mm f2 lens

If i take photos with both lenses mounted to an aps-c camera, and i keep the shutter speed and ISO the same, will the resulting images have the same brightness? Or will the full-frame lens images be darker?

My reasoning is as follows:

1. The light of the full frame lens is projected to a larger area (because the projection would have to cover a full-frame sensor) than the aps-c lens (whose projection covers exactly an aps-c sensor).
2. Therefore a lot of the gathered light of the full frame lens is wasted while mounted on the aps-c body.
3. Both have the same aperture, which means that they let the same amount of light in.
4. Because both lenses gather the same amount of light but the full frame wastes more, id assume the image taken with the full-frame lens to be darker. Is this correct?

Answer 1

A larger image circle is more light, but that additional light only exists in the areas not recorded by the crop sensor. Essentially, the APS lens is just cropping the image circle before the sensor gets a chance to.

I.e. the light emitted from a point in a scene must return to that point in the image in order for the image to be in focus. So no matter how much of the scene you record by changing the sensor size, the exposure (light per area) does not change.

A larger image is also more light from the recorded area. I.e. photographing a lightbulb with the same composition on a FF sensor is more light than recording it the same on a crop sensor... the exposure/light per area is the same, but the area occupied by the bulb is physically larger. This is where the low light benefit of larger sensors comes from.

Answer 2

The brightness of the image formed by a lens is the same regardless of the size of the sensor behind it, assuming the image circle fully covers the sensor.

An APS-C sensor behind a full frame lens is sampling a small portion of the image circle. This is effectively the same as cropping an image captured using that lens in front of a full frame sensor, hence the name "crop sensor." Cropping an image does not change anything about the exposure, so the exposure setting you use ought to be the same.

1 is correct. 2 is also correct, because the image circle cast by a full frame lens is much larger than the ASP-C sensor.

3 is technically incorrect. In the area that the lenses' image circles overlap, the brightness is the same, but the full frame lens casts a much larger circle so that it can cover the larger sensor.

You can see this more clearly by going the other way, placing an APS-C lens onto a full frame body. You will see a circle in the middle which is correctly exposed, but the edges are black. The APS-C lens doesn't project a large enough image circle to cover the larger sensor. However, within the center of that circle, the image is the same brightness as an equivalent full frame lens.

Answer 3

The full frame sensor will not be brighter under the same exposure conditions (Same light in scene, same focal length and f-number, same exposure time, etc.). It will collect more light, but it will also spread that light over an equally proportionally larger area. The brightness, which is defined as the amount of light energy per unit area, will be the same.

The advantage of the larger pixels (assuming both sensors have the same number of pixels) will not be in increased brightness, but in reduced noise (due to the averaging of the random nature of light - what we call shot noise - over a larger area) and increased dynamic range of the larger pixels on the FF sensor (due to higher full well capacity for the same thickness silicon wafer).

Answer 4

Every lens vignette, only the central portion of the projected image cast by the lens is pictorially useful. This central portion is called the circle of good definition. For each format size, there is a focal length of choice we label as “normal”. The vignette of a “normal” is unlikely to be concerning. This will be a focal length approximately equal to the corner-to-corner measure (diagonal) of the format. For the full frame 24mm by 36mm, will be 43.3mm. By tradition this value is rounded up to 50mm. c The APS-C (Advanced Photo System – Classic) measures about 16mm by 24mm. The diagonal measure of this rectangle and the “normal” focal length is approximately 30mm.

The difference between the two formats: The APS-C is 66% of the size of a full frame. The full frame is 1.5X (150%) larger.

Now the circle of good definition of a 50mm focal lens is adequate to cover a full frame and more than adequate to cover the APS-C format.

As to your reasoning point #1 – it is moot!

As to your reasoning point #2 – The spillover of a 50mm focal length lens is far greater than the area of both formats. Spillover must be dealt with. If not, the internal parts of the camera’s light path will likely reflect stray imaging rays. These would bathe the image recording area during the exposure. This stray light induces flare. Flare is devastating as it lowers the natural contrast of the projected image. To deal with stray light, the interior of camera is painted flat black to deaden reflections. Plus, the interior walls have baffles that mitigate reflections.

As to your reasoning point #3 – Spillover is always present in every optical system. The loss of this light energy in itself is moot except, if not controlled it is the source of flare which would induce a loss of contrast if not controlled.

As to image brightness - Any lens operating at the same f-number as another, delivers an image of equal brightness (within reason for pictorial usage). In other words the f-number (focal ratio) is valid regardless of focal length and working aperture diameter. Differences in the transparencies of the lens elements and surface reflection loss plays a part. For critical work we then resort to T-stops which are calibrated via an actual light intensity measurement.