Question

A person stands straight in front of a convex mirror at a distance of 20 m away from it. He sees his erect image whose length is 1/5th of his real height. Find the focal length of the convex mirror.

• A. 4 m
• B. 6 m
• C. 5 m
• D. 8 m

Answer 1

The correct option is C 5 m

Given : u = -20 m;
magnification (m) = 1/5

$Magnification=\frac{-v}{u}=\frac{h_i}{h_o}$
$\frac{-v}{-20}=\frac{1}{5}$

=> v = 4 m

Now, using mirror formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{4}+\frac{1}{-20}=\frac{1}{f}$
$\frac{1}{f}=\frac{1}{5}$

=> f = 5 m