Question

r=2f proof for convex mirror

Answer 1

Answer:

The angles in the triangle(CFX) are vertically opposite and corresponding angles from the angles of reflection and incidence.

From the diagram it is apparent that XF does not equal PF.

However, when point X is closer to the principal axis, XF approaches the size of PF.

So for rays close to the principal axis, we can say that XF = PF.

In other words,

XC = PF + FC

r = f + f

r = 2f

Explanation:

Refer picture for diagram