Question

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​

Answer 1

Given:

A man stands with his nose 8 cm from a concave shaving mirror of radius 32 cm.

To find:

Image distance from mirror ?

Calculation:

• We know that focal length is half of radius of curvature , so f = R/2 = -32/2 = -16 cm.

Now, applying MIRROR FORMULA:

$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$\implies \dfrac{1}{ (- 16)} = \dfrac{1}{v} + \dfrac{1}{( - 8)}$

$\implies - \dfrac{1}{ 16} = \dfrac{1}{v} - \dfrac{1}{8}$

$\implies \dfrac{1}{v} = \dfrac{1}{8} - \dfrac{1}{16}$

$\implies \dfrac{1}{v} = \dfrac{2 - 1}{16}$

$\implies \dfrac{1}{v} = \dfrac{1}{16}$

$\implies \: v = 16 \: cm$

So, image of nose from mirror is 16 cm.