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Jul 8, 2015 at 21:18 comment added Brandon Dube If a lens is f/2.8, it provides the same light per area regardless of focal length and image size. I.e it will provide the same amount of light to the centermost 1mm*1mm area as it will to a corner 1mm*1mm area, ignoring vignetting and natural cos^4 light falloff.
Jul 8, 2015 at 19:56 comment added feetwet OK: It sounds like your statement is holding the lens constant. But if we assume as in the OP that the lens was designed for the sensor in each case (so the lens for the 30mm sensor has a 30mm spread while the lens for the 12mm sensor has a 12mm spread), then are we talking about different f numbers? (Again, assume same FoV, objective size, and overall lens transmission.) Or do we have the same f number but more illumination per mm^2 on the smaller sensor?
Jul 8, 2015 at 19:32 comment added Brandon Dube Not quite. Imagine an ultra-wide angle lens and a supertele. The supertele spreads maybe 4 degrees across 12mm, right? An ultra-wide spreads 40 degrees or more across that same 12mm. Thus, the magnification at the sensor is very very high. If you used a positive lens behind the same base objective to concentrate the previous image size onto a smaller area, you will get a faster f/number and brighter image. If you don't and let the excess be excess, it is identical to cropping from the bigger image.
Jul 8, 2015 at 18:06 comment added feetwet Perhaps the OP made an unnecessary assertion and has his assumptions backwards? Presumably, given the same objective lens size, and holding field of view constant, a smaller sensor will get a brighter image because exit pupil can be smaller. I.e., the incident light is the same but it can be concentrated more on a smaller sensor area, right? (This assumes transmission is the same through both lenses.)
Jul 8, 2015 at 17:07 vote accept Echo88
Jul 6, 2015 at 15:48 history answered Brandon Dube CC BY-SA 3.0