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A cylindrical tube filled with water μ w = 4 3 is closed at its both ends by two thin, silvered plano-convex lenses, as shown in the figure. Refractive index of lenses L 1 and L 2 are 2.0 and 1.5 , while their radii of curvatures are 5 cm and 9 c m , respectively. A point object is placed somewhere at a point O on the axis of the cylindrical tube. If it is found that all the images formed by multiple refractions and

Options

  1. A8 c m
  2. B18 c m
  3. C10 c m
  4. D14 c m

Correct answer

B. 18 c m

Step-by-step solution

For the lens L 1 , the ray must move parallel to the axis after refraction, for the image to coincide with the object. μ 1 ∞ + μ w x = μ 1   - μ w R 1 , where x is the distance of the object from the lens L 1 4 3 x = 2 - 4 3 5 ⇒ x = 10   cm For the lens L 2 , the ray must appear to come from the centre of curvature after refraction, for the image to coincide with the object. μ 2 - R 2 + μ w y = μ 1   - μ w ∞ , where y is the distance of the ob

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