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the curvature radii of a concavo-convex glass lens are 20 cm and 60 cm . The convex surface of the lens is silvered. With the lens horizontal, the concave surface is filled with water. The focal length of the effective mirror is ( μ of glass = 1 . 5 , μ of water = 4 3 )

Options

  1. A9 0 1 3 cm
  2. B8 0 1 3 cm
  3. C2 0 3 cm
  4. D4 5 8 cm

Correct answer

A. 9 0 1 3 cm

Step-by-step solution

R = 60   cm , R 2 = 20   cm Let P 1 be power of lens of water , P 2 be power of glass lens, and P 3 be power of concave mirror P eq =   2 P 1   +   2 P 2   +   P 3 1 - f eq = 2 f 1 + 2 f 2 - 1 f 3                        ....(1) for the lens of water 1 f 1 = 4 3 - 1 1 ∞ - 1 - 6 0 1 f 1 = 1 1 8 0 for glass lens 1 f 2 = ( 3 2 - 1 ) ( 1 - 6 0 - 1 - 2 0 ) 1 f 2 = 1 6 0 For concave mirror f 3 = R 2 f 3 = - 10   cm 1

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