Why is the focal length of a plane mirror infinity?

Answer 1

In a plane mirror, the radius of curvature is infinitly long, so the focus will be at infinity. Another way to say it is that a plane mirror has no curvature, and as curvature becomes increasingly small, focal length becomes increasingly long. At a curvature of zero, focal length becomes infinite.

Focal length(f) is given by f=R/2 where R is radius of curvature..

Once again, it's infinity! See answer to your question on radius of curvature. Plug infinity (radius of curvature) into your mirror equation to get the focal length, which will also be infinite. A flat mirror does not focus incoming parallel beams.

That's because if you say its at infinity it means it does exist in a finite

distance, that is instead of saying it does exist its taken at infinite distance for only theoretical importance and not for practical observance. Focal length is half of radius of curvature of the mirror. So bigger the circle gets the more its radius will be. So in the same way as the curvature of the sphere gets less and less its focal length increases, so

when it becomes totally flat the focal length will become infinite so it means it has no existence but it has only theoretical importance.

It same as taking the formation of image of an object at principal focus to be at infinite distance rather than saying it does not form ( that is both mean the same).

hope my answer is satisfactory

Answer 2

Because a ray of light (i.e. a photon) will just bounce back and forth forever -

I assume you realize that it would take forever to actually form "infinite images".