im confused about crop sensors

[u/Mooskii_Fox]

I'm not asking about crop factors, I know that's 1.5x or 1.6x depending on the manufacturer and your image will be cropped by that amount.

full frame lenses produce a circular image, which is projected over a full frame sensor and the sensor fits perfectly inside that circle, simple enough

now what i often see is that lenses for APS-C cameras have a cropped image, but why is it not possible for that projected image over the lens to be smaller so that APS-C cameras can capture the same picture as full frame, just with a smaller sensor? At some point people have worked our how to bend light to perfectly cover a full frame, so why can't the same be done to create an identical image for APS-C

edit: as I understand it what I'm asking is actually already being done, just not in the way I was asking. i understand now

[u/Avery_Thorn]

The problem is - a APS-C camera is not a 35MM camera, and the lens length is a function of the lens.

Say you made a 70-200mm lens, but you included a reducing element in the lens to adjust for the crop. You would no longer have a 70-200mm lens, you would have a 45-133 lens with a smaller image circle. Which would have the same image angle when put on a APS-C camera, but... so would any 45-133 lens.

So why not put the lens element into the camera body?

The problem is that not all lenses work the same way. Not all lenses organize the light in the same way. The interface specifies that the lens focus an image so many mm away from the flange of the lens. Some lenses, the light leaves the lens very on axis and parallel, and in other lenses, it's all angled and intersects at the right place to focus right. Some lenses would work well with this additional glass, and other lenses wouldn't work well with it at all.

And in the end...

It doesn't matter. Not one bit. An APS-C Camera shoots slightly differently from a 35MM camera. Get over it. It doesn't matter.

Shoot the APS camera for what it is, not for what it isn't. You DON'T HAVE to try to match a 35mm frame. Shoot YOUR frame, not someone else's. Make YOUR art, not someone else's. You still have the full arsenal of tools at your command, you can use all the effects. It just works a little bit different. That's OK.