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Question

A ray incident at a point at an angle of incidence θ enters into a glass sphere placed in air which is reflected and refracted at the farther surface of the sphere as shown in the figure. The angle between reflected and refracted rays at this surface is 900. If refractive index of the sphere is 3, the angle θ is :
76313.jpg
  1. π4
  2. π3
  3. 2π3
  4. π6

A
π3
B
π4
C
π6
D
2π3
Solution
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Applying Snell's law on the 2 surfaces,

sinθ=3sinr

Where, r is the angle of refraction.

Applying on the second surface,
sinr=cosθ

Equating the 2 terms,

sinθ=3cosθ

Thus, tanθ=3

Or, θ=600

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76313.jpg
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