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

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Solution

Given:
Object distance in the first case, $u_{1} = 60 c m$
Distance between two image locations, $d = 40 c m$

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.
$60 - x = x + 20$
$x = 20 c m$

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

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