Question

A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is 2.0. What is the magnification when the convex side is used as a mirror, the object remaining the same distance from the mirror?

Answer 1

The mirror equation is
1/ p + 1/ i = 1 / f  ......(1)
P is the object distance, i is the image distance, and f is the mirror's focal length.
When the concave side is used as a mirror, the magnification is
m = - i / p
2 = - i / p
i = - 2 p
Substituting in equation (1)
1/ p + (- 1 / 2 p) = 1 / f
1 / f = 1 / 2 p
f = 2 p
So for the mirror, the focal length is 2 times the object distance
For the second case in which the object is placed in front of the convex mirror, the mirror equation is 1/ p + 1/ i₂ = 1 / f
The object distance and the focal length are same as that of the concave mirror, in magnitude. But for the convex side, the focal length is negative
We know that f = 2 p
1/ p + 1 /i₂  = - 1/ 2 p
1/ i₂  = - (1 /2 p + 1 /p)
1 / i₂  = - 3 / 2 p
i₂  = - 2 p / 3
the magnification of the object is
m = - i₂  / p
m = - (- 2 p/ 3) / p
m = 2 / 3