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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 .

Options

  1. AI → P , II → R , III → Q , IV → T
  2. BI → Q , II → P , III → T , IV → S
  3. CI → P , II → T , III → R , IV → Q
  4. DI → T , II → S , III → Q , IV → R

Correct 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 =

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