Relative pixels on the target

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Jonathan
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I am struggling with basic maths I think.

So, a 400mm lens (though focal length irrelevant for this calc I assume)

A 21mp full frame camera vs a 10mp 1.3x crop camera, taking a photo of a bird from a fixed distance. Which has more pixels on the bird?

Thanks
Jonathan
 
The full frame camera. I think.
The way I work it out is that the ff camera has twice the pixel density of the 1.3X crop.
So for any area, lets say 2mm square, the ff camera has 2x as many pixels.
So on the 10mp camera the bird would have to be twice as big to cover the same number of pixels but it's only 1.3x as big.

Actually I think that's wrong because the ff camera doesn't have twice the pixel density, it has twice the number of pixels spread over a slightly larger area.
Think the same equation still applies though so that if the crop sensor was half the size of the ff sensor and had half the pixels it'd have the same number on target but half the pixels and only a 1.3x crop = less pixels on target.
 
Full frame in that example. 12.4 vs 10mp. Not that significant. You need about 50% difference to notice much.

Divide 21 by crop factor squared.
 
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