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A plano-convex lens μ = 3 2 has a radius of curvature R = 15 c m and is placed at a distance z from a concave lens of focal length 20 cm as shown. At what distance x 0 should a point object be placed from the plano-convex lens, so that position of the final image is independent of z ?

Options

  1. A20 c m
  2. B30 c m
  3. C40 c m
  4. D60 c m

Correct answer

B. 30 c m

Step-by-step solution

The position of the final image will be independent of z , only if the rays of light are incident on the concave lens as a beam parallel to the principal axis. This will be possible only when the object is kept at focus of the plano-convex lens. ∴ 1 x 0 = 1 f 1 = ( μ - 1 ) 1 R 1 - 1 R 2 = 3 2 - 1 1 15 - 1 ∞ ⇒ x 0 = 30 c m

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