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Q.

At what distance from a convex mirror of focal length 2.5 m should a boy stand so that his image has a height equal to half the original height

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a

7.5 m from the mirror

b

10 m from the mirror

c

2.5 m from the mirror

d

5 m from the mirror

answer is A.

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Detailed Solution

m = - \frac{v}{u} = \frac{1}{2}

$v = - \frac{u}{2}$

$we know$

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$\frac{1}{f} = \frac{1}{- u/2} + \frac{1}{u}$

$\frac{1}{2.5} = \frac{1}{u} - \frac{2}{u}$

$\frac{1}{2.5} = \frac{- 1}{u}$

$u = - 2.5 cm$

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