A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will b

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Solution

Q.
A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be [2021]

1 30

2 25

3 15

4 50

Ans.
(3)

Given : $f_{1} = 20 cm, f_{2} = - 5 cm$

Equivalent focal length, $f = \infty$

(As the rays are parallel)

By using Newton’s displacement formula,

$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}} \Rightarrow \frac{1}{\infty} = \frac{1}{20} - \frac{1}{5} - \frac{d}{20 \times (- 5)}$

$0 = \frac{5 - 20 + d}{20 \times 5} \Rightarrow d = 15 cm$

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