Question

A person is standing in front of a plane mirror at $60cm$ from it. Suddenly the mirror moves by some distance towards him. It was found that the final image also moves by $40cm$ from the initial position towards the mirror. Find the distance moved by a mirror?

• A. $40cm$
• B. $15cm$
• C. $20cm$
• D. $80cm$

Answer 1

The correct option is C

$20cm$

Given:
Object distance in the first case, $u_1=60cm$
Distance between two image locations, $d=40cm$

Let the distance moved by the mirror be $x$
From the given figure,
New image distance from the mirror:
$v_2=x+20$
New object distance from the mirror:
$u_2=60–x$

For plane mirrors, image distance and object distances are equal.
$60–x=x+20$
$x=20cm$