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A thin convex lens of focal length f is put on a plane mirror as shown in the figure. When an object is kept at a distance a from the lens-mirror combination, its image is formed at a distance a 3 in front of the combination. The value of a is:

Options

  1. A2 f
  2. B3 2 f
  3. C3 f
  4. Df

Correct answer

A. 2 f

Step-by-step solution

Equivalent power of combination is P e f f = 2 P l e n s + P m i r r o r ...(i) ∵ P m i r r o r   = 0 for plane mirror and P l e n s = 1 f Also combination behaves as a mirror. So. P e f f = 1 f m i r r o r In equation (i) - 1 f m i r r o r   = 2 f ⇒ f m i r r o r = - f 2 By mirror formula 1 f m i r r o r   = 1 u + 1 v Here u =   - a ,   v = - a 3 ,   f m i r r o r =   - f 2 ⇒ - 2 f = 1 - a + 3 - a = - 4 a ⇒ - 2 f = - 4 a ⇒ a = 2 f

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