Question

A spherical surface is mirrored on both sides. When you look at the convex side, you see yourself at +0.75 magnification. If you flip the mirror to its concave side, at what magnification do you see yourself (assuming the distance from your face remains the same)?

a. +7.78

b. +5.50

c. +2.17

d. +1.50

e. +1.21

Answer 1

For the concave side of the mirror the magnification is m = -v/u where v and u are image and object distances from the mirror. Here m = +0.75 so v = -0.75u. v and u are related to the focal length f by

1/u+1/v = 1/f.

Substitute for v :

1/u-1/0.75u = -0.33/u = 1/f.

When the convex side of the mirror is towards the object, then f is replaced by -f. u is the same but v is different :

1/u+1/v' = -1/f

1/v' = -1/f-1/u = -(-.33)u-1/u = -0.67/u

v' = -u/0.67

so the magnification when the convex side is used is

m' = - v'/u = -(-1/0.67)

= +1.50 (option d)