A boy standing in front of a concave mirror of focal length $20 m$ moves $10 m$ towards the mirror. What is the distance moved by his image if he is initially standing at a distance of $25 m$ from the pole of the mirror?

60 m

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160 m

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150 m

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100 m

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Solution

The correct option is B $160 m$
Given,
object distance, $u = - 25 m$
focal length, $f = - 20 m$
image distance, $v = \frac{u f}{u - f}$
$⟹ v = \frac{- 25 \times - 20}{- 25 - (- 20)}$
$⟹ v = - 100 m$
the boy has moved $10 m$ towards the mirror
$⟹ u^{^{'}} = 25 - 10 = 15 m$
image distance, $v = \frac{u f}{u - f}$
$⟹ v = \frac{- 15 \times - 20}{- 15 - (- 20)}$
$⟹ v = 60 m$
Positive sign of image distance is showing that image is forming behind the mirror.
so,distance moved by the image $= 100 + 60 = 160 m$
$⟹ 160 m$ away from the mirror.

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A boy standing in front of a concave mirror of focal length 20 m moves 10 m towards the mirror. What is the distance moved by his image if he is initially standing at a distance of 25 m from the pole of the mirror?

A boy standing in front of a concave mirror of focal length $20 m$ moves $10 m$ towards the mirror. What is the distance moved by his image if he is initially standing at a distance of $25 m$ from the pole of the mirror?