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A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of 4R in front of spherical interface. The magnitude of the magnification of point source image is _______.

Options

  1. A1.66
  2. B2.33
  3. C2.66
  4. D1.33

Correct answer

A. 1.66

Step-by-step solution

Given: Refractive index of the first medium, n₁ = 1 Refractive index of the second medium, n₂ = 1.4 = 7 5 Object distance, u = -4R Radius of curvature of the spherical interface, R = +R (since the surface is convex towards the rarer medium) Using the formula for refraction at a single spherical surface: n₂ v - n₁ u = n₂ - n₁ R Substituting the given values: 1.4 v - 1 -4R = 1.4 - 1 R 7 5v + 1 4R = 0.4 R 7 5v + 1 4R = 2 5R 7 5v = 2 5R - 1 4R 7 5v = 8 - 5 20R = 3 20R v = 7 20R 5 3 = 28R 3 The transverse magnification

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