Question

A convex mirror forms an image one-fourth the size of the object. If object is at a distance of $0.5m$ from mirror the focal length of the mirror is

• A. $0.16m$
• B. $-1.5m$
• C. $0.4m$
• D. $-0.4m$

Answer 1

Answer: (A)

$0.16m$

Given : $u=-0.5m$
Convex mirror forms erect image of real object.
Using, $\frac{h_i}{h_o}=-\frac{v}{u}$
Or $\frac{1}{4}=-\frac{v}{(-0.5)}$
$⟹v=0.125m$
Using mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\therefore$ $\frac{1}{0.125}+\frac{1}{-0.5}=\frac{1}{f}$
$⟹f=0.16m$