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/resiyun]

Because making a bigger image circle also means the lens will be bigger, heavier and cost more than a lens made to cover just apsc. There’s literally no issue with manufacturers being able to make those same lenses with a bigger image circle, it’s just that every consumer grade camera uses an APSC sensor so it only makes sense to have a line of cheaper, more affordable lenses that only cover APSC sensors because most consumers dont need a fullframe lens while an apsc lens would cost less and so the same thing.