A mirror is used to produce an image with magnification of . If the distance between object and its image is 40 cm, then the focal length of the mirror is [2025]

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Solution

Q.
A mirror is used to produce an image with magnification of $\frac{1}{4}$ . If the distance between object and its image is 40 cm, then the focal length of the mirror is [2025]

1 10 cm

2 12.7 cm

3 10.7 cm

4 15 cm

Ans.
(3)

$m = - \frac{v}{u} = - (\frac{v}{- u}) = \frac{v}{u}$

$\frac{1}{4} = \frac{v}{u} \Rightarrow u = 4 v$

$v + u = 40 \Rightarrow 5 v = 40$

v = 8 cm and u = 32 cm

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{8} - \frac{1}{32} = \frac{1}{f}$

$\Rightarrow f = \frac{32}{3} = 10.7 cm$

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