A boy is observing his image in a plane mirror. The distance between the mirror and his image is $10 m$ . If he moves $2 m$ towards the mirror, then the distance between the boy and his image will be:

14 m

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16 m

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20 m

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24 m

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Solution

The correct option is B $16 m$
Given:
Initial image distance, $I_{1} = 10 m$
Final object distance $(O_{2})$ is $2 m$ less than the original object distance $(O_{1})$ :
$O_{2} = O_{1} - 2$

For plane mirror, image distance equals object distance for any given instance.
At initial position,
$O_{1} = I_{1} = 10 m$

At final position,
Object distance is:
$O_{2} = 10 - 2 = 8 m$
Image distance is:
$I_{2} = O_{2} = 8 m$
Hence, distance between the boy and his image is:
$d = O_{2} + I_{2} = 16 m$

Hence, the distance between the boy and his image becomes equal to $16 m$ , as is also evident from the figure below.

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