Question

A convex spherical mirror, whose focal length has a magnitude of 21.8 cm, is to form an image 12.2 cm behind the mirror. (a) Where should the object be placed?
(b) What is the magnification of the mirror?

Answer 1

Explanation:

Focal length of convex mirror, f = -21.8 cm

Image distance, v = -12.2 cm

(a) Let u is the object distance. Using mirror's formula :

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

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

$\dfrac{1}{u}=\dfrac{1}{-21.8}-\dfrac{1}{-12.2}$

u = 27.70 cm

(b) The magnification of the mirror is the ratio of image distance to the object distance, $m=\dfrac{-v}{u}$

$m=-\dfrac{-12.2}{27.70}$

m = 0.44

Hence, this is the required solution.