Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is: [2023]

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Solution

Q.
Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is: [2023]

1 40 cm

2 60 cm

3 160 cm

4 100 cm

Ans.
(3)

$by mirror formula \frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

$\frac{1}{v_{1}} + \frac{1}{- 15} = \frac{1}{- 20}$

$\frac{1}{v_{1}} = - \frac{1}{20} + \frac{1}{15} = \frac{- 3 + 4}{60} \Rightarrow v_{1} = 60 cm$

$\frac{1}{v_{2}} + \frac{1}{- 25} = \frac{1}{- 20}$

$\frac{1}{v_{2}} = \frac{- 1}{20} + \frac{1}{25} = \frac{- 5 + 4}{100} = \frac{- 1}{100}$

$\Rightarrow v_{2} = - 100 cm$

$d = 60 + 100 = 160 cm$

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