Question

A ray of light is incident at an angle i on one face of a thin angled prism. The ray emerges normally from the other face. Refractive index of the glass prims is n and angle of prism is A. The value of i is ______.

Options

• An

• A²n

• An²

• \[\frac{1}{\text{An}}\]

Answer 1

A ray of light is incident at an angle i on one face of a thin angled prism. The ray emerges normally from the other face. Refractive index of the glass prims is n and angle of prism is A. The value of i is An.

Explanation:

Consider the figure shown below

ln Δ POR,

α = 180° - 90° - A

α = 90° - A

Also, r + α = 90°

⇒ r = 90° - α = 90° - 90° + A

or r = A

Using Snell's law,

µ₁ sin i = µ₂ sin r

(1) sin i = n sin A (given, µ₂ = n for glass prism)

⇒ sin i = n sin A

For small angle,

sin i ≃ i and sin A ≃ A

∴ i = nA