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A transparent solid cylindrical rod has a refractive index of 2 3 . It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure. The incident angle θ for which the light ray grazes along the wall of the rod is

Options

  1. Asin - 1 ⁡ 1 2
  2. Bsin - 1 ⁡ 3 2
  3. Csin - 1 ⁡ 2 3
  4. Dsin - 1 ⁡ 1 3

Correct answer

D. sin - 1 ⁡ 1 3

Step-by-step solution

From Snell's law, μ air sin θ = μ cylider sin 90 ° – θ C ⇒1×sin θ = 2 3 × cos θ C But, sin ⁡ θ C = 1 μ c y l i n d e r = 3 2 Therefore cos ⁡ θ C = 1 2 ⇒sin θ = 2 3 . 1 2 = 1 3 ⇒ θ = sin – 1 ⁡ 1 3

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