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To find the focal length of a convex mirror, a student records the following data: Object pin Convex Lens Convex Mirror Image Pin 22.2 cm 32.2 cm 45.8 cm 71.2 cm The focal length of the convex lens is f 1 and that of mirror is f 2 . Then taking index correction to be negligibly small, f 1 and f 2 are close to:

Options

  1. Af 1 = 7.8 c m f 2 = 12.7 c m
  2. Bf 1 = 12.7 c m f 2 = 7.8 c m
  3. Cf 1 = 15.6 c m f 2 = 25.4 c m
  4. Df 1 = 7.8 c m f 2 = 25.4 c m

Correct answer

A. f 1 = 7.8 c m f 2 = 12.7 c m

Step-by-step solution

Take f 2 = 12.7 1 f = 1 v + 1 u 1 12.7 = 1 25.4 + 1 u 1 12.7 = 1 25.4 = 1 u u = 25.4 = v ′ 1 f = 1 v - 1 u 1 f 1 = 1 25.4 + 13.6 + 1 10 1 f 1 = 1 39 + 1 10 1 f 1 = 390 49 = 7.96 The closest answers is (1) as option (3) and (4) are not possible.

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