> Would the resulting photo be skew out of proportion?
No, just some of the light that passes through the lens doesn’t reach the rectangular sensor. It isn’t taking the input from the circular lens and warping it to fit the sensor, it is being trimmed.
You could in theory have an oval lens, or even a square lens to match the square sensor. But they would be much harder to make than round lenses and there is really no point.
You can make a lens whatever shape you want to, and it will still make a similar^1 image. It just happens that a lens’ shape has circular symmetry, so it is easiest to make it in a circle.
And once you’ve got a circle, if you chop part of it off you’ll end up with a smaller lens which typically reduces quality.
1. There are artrfacts from a non-circular aperture but they tend to be minor. You see them as streaks from bright lights mostly.
The sensor might be a rectangle 24x36mm but the lens projects an image with a larger circle… at least 42mm but maybe even 50mm in diameter (it’s actually not exactly easy to measure as the edges of the image circle are very fuzzy and soft, but the inside sharp and bright area for “full frame” camera lens would be at least 42mm). The sensor only captures a rectangular area inside the image that is projected by the lens. This is why if you take the same lens and go from a 24x36mm “full frame” sensor to a 14x22mm “APS-C” sensor the image is more “telephoto” or “tighter” as the smaller sensor “crops into” or only captures a smaller area of the lens image.
Oval lenses would be weird and would either stretch the image like an anamorphic lens or make it focus weird (if you have an astigmatism your lenses actually have a slight cylindrical bow to them to correct the focus issues with astigmatism)… depends a bit on the specifics of how the lens is designed.
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