A man stands with his nose 8 cm from a concave shaving mirror of radius 32 cm.The distance from the mirror to the image of his nose is:
A)8 cm
B)12 cm
C)16 cm
D)24 cm
E)32 cm

Question

Quizplus · Accepted Answer

Using the mirror formula, we have:

1/f = 1/o + 1/i

where f is the focal length of the mirror (which is -16 cm for a concave mirror of radius 32 cm), o is the distance of the object (the man's nose) from the mirror (which is 8 cm), and i is the distance of the image from the mirror (which is what we want to find).

Substituting the values, we get:

1/-16 = 1/8 + 1/i

Simplifying, we get:

-1/16 = 1/i - 1/8

Multiplying both sides by 16i, we get:

-i = 2i - 2

Solving for i, we get:

i = -2(-16) / 1 = 32 cm

So the distance from the mirror to the image of his nose is 32 cm.

Therefore, the answer is C) 16 cm.

A Man Stands with His Nose 8 Cm from a Concave