Curved mirrors question?

Question

what happens when parallel rays are directed at a circular mirror parallel to the axis of symmetry but displaced sideways?

Answer 1

Not sure what you mean by "displaced sideways".  Assuming you mean "parallel to the axis of symmetry but not ON the axis", it depends on whether the mirror is convex or concave.

Convex (mirror ball): light bounces away as if it were coming in a straight line from the focal point of the mirror, which is behind the mirror.  No particular nifty effect.

Concave (mirror cup): light bounces back through the focal point.  So all the parallel beams end up going through the focus, and you can really get things cooking there.