Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens. [2023]

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Solution

Q.
Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens. [2023]

Ans.
(100)

$f_{1} = 20 cm, f_{2} = 20 cm$

$1st refraction in L_{1} (I_{1})$

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} - \frac{1}{\infty} = \frac{1}{f}$ $∴$ $v = f$

$2nd refraction in L_{2}$

$I_{1} \to object, I_{2} \to image also, u = - 40 cm and f = 20 cm$

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} - \frac{1}{(- 40)} = \frac{1}{20}$ $∴$ $v = 40 cm$

$Correct Answer is 100 .$

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