Question

A man standing 1.60 m in front of a shaving mirror produces an inverted image 20.6 cm in front of it. How close to the mirror should he stand if he wants to form an upright image of his chin that is twice the chin's actual size?

Answer 1

The initial information about object distance and image distance lets us determine the focal length of the mirror --

Notice that d_i = + 20.6 cm since the image is in front of the mirror (and since it is inverted). The fact that d_o = 160 cm should be easy.

f = 18.3 cm

To form an upright image means M > 0; to have an image twice the size of the object (or chin) means M = 2. Either also requires a virtual image. Thus,

d_i = - 2 d_o

Essentially, we have two equations with two unknowns,

M = -di/do = 2

1/f = 1/do + 1/di

1/18.3 = 1/do + 1/di

1/18.3 = 1/do + 1/(-2do)

1/18.3 = 1/2do

2do = 18.3

do = 9.15 cm