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JEE Advanced Physics Ray Optics 2022 JEE Advanced 2022 (Paper 1)

JEE Advanced Physics Question (2022) — Solution

Question

List I contains four combinations of two lenses ( 1 and 2 ) whose focal lengths (in cm ) are indicated in the figures. In all cases, the object is placed 20 cm from the first lens on the left, and the distance between the two lenses is 5 cm . List II contains the positions of the final images.   List-I   List-II (I) (P) Final image is formed at 7 . 5 cm on the right side of lens 2 . (II) (Q) Final image is formed at 60 . 0 cm on the right side of lens 2 . (III) (R) Final image is formed at 30 . 0 cm on the left side of lens 2 . (IV) (S) Final image is formed at 6 . 0 cm on the right side of lens 2 .     (T) Final image is formed at 30 . 0 cm on the right side of lens 2 . Which one of the following options is correct?

Options

  1. A. I → P , II → R , III → Q , IV → T
  2. B. I → Q , II → P , III → T , IV → S
  3. C. I → P , II → T , III → R , IV → Q
  4. D. I → T , II → S , III → Q , IV → R

Answer

A. I → P , II → R , III → Q , IV → T

Step-by-step solution

I u = – 20   cm   f 1 = + 10   cm Using the lens formula, 1 v - 1 u = 1 f ⇒ 1 v 1 + 1 20 = 1 10 ⇒ 1 v 1 = 1 10 - 1 20 ⇒ v 1 = 20   cm For second lens  u = v 1 - 5 = + 15   cm ,  f 2 = + 15   cm ⇒ 1 v - 1 u = 1 f 2 ⇒ 1 v - 1 15 = 1 15 ⇒ 1 v = 2 15 v = + 7 . 5   cm (from lens 2 ) Therefore,  I → P (II)  Similarly, u = - 20   cm , f = + 10   cm 1 v + 1 20 = 1 10 ⇒ 1 v = 1 10 - 1 20 ⇒ v = 20   cm For second u = v 1 - 5 = + 15 cm ,  f = - 10 cm 1 v - 1 u = 1 f ⇒ 1 v - 1 15 = - 1 10 ⇒ 1 v = - 1 10 + 1 15 = - 3 + 2 30 ⇒ 1 v = - 1 30 v = - 30   cm II → R (III)  u = - 20 ,  f = + 10 cm 1 v + 1 20 = 1 10 ⇒ 1 v = 1 10 - 1 20 = 1 20 ⇒ v = 20 cm For second, ⇒   u = 15 cm f = –   20 cm 1 v - 1 15 = - 1 20 ⇒ 1 v = - 1 20 + 1 15 = - 3 + 4 60 = 1 60 v = 60   cm III → Q (IV)  u = – 20 cm ,  f = – 20 ⇒   1 v - 1 u = 1 f ⇒ 1 v + 1 20 = - 1 20 v = - 10 cm For second u = – 15 cm f = 10 cm 1 v - 1 u = 1 f ⇒ 1 v + 1 15 = 1 10 ⇒ 1 v = 1 10 - 1 15 = 3 - 2 30 = 1 30 v = 30 cm IV → T

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