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Physics

The refracting angle of prism is 60° and the angle of deviation is 30°. In the position of minimum deviation, the angle of incidence i1 and the angle of emergence i2 are :

  1. i1 = 45°, i2 = 30°
  2. i1 = 30°, i2 = 45°
  3. i1 = 45°, i2 = 45°
  4. i1 = 30°, i2 = 30°

Refraction Plane Surfaces

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Answer

i1 = 45°, i2 = 45°

Reason — Given

  • A = 60°
  • δ = 30°

In the position of minimum deviation for a prism, the path of light inside the prism is symmetrical. Therefore, the angle of incidence equals the angle of emergence, i.e., i1 = i2.

The relation between the angle of deviation δ, refracting angle A, and angle of incidence i is given by,

δ=2iA\text δ = 2\text i − \text A

On putting values,

30°=2i60°2i=30°+60°i=90°2i=45°\Rightarrow 30° = 2\text i - 60° \\[1em] \Rightarrow 2\text i = 30° + 60° \\[1em] \Rightarrow \text i = \dfrac{90°}{2} \\[1em] \Rightarrow \text i = 45°

Thus, i1 = i2 = 45°

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