Question

The angle of deviation through a prism is minimum when

(A) Incident ray and emergent ray are symmetric to the prism.
(B) The refracted ray inside the prism becomes parallel to its base
(C) Angle of incidence is equal to that of the angle of emergence
(D) When angle of emergence is double the angle of incidence
Choose the correct answer from the options given below :

• A. Statements (B) and (C) are true
• B. Only statements (A) and (B) are true
• C. Statements (A), (B) and (C) are true
• D. Only statement (D) is true

Hint:

At minimum deviation \(i = e\) and \(r_1 = r_2 = A/2\), so the ray inside the prism is parallel to the base and the path is symmetric.

Answer 1

The Correct Option is C

For a prism, the deviation is \(\delta = i + e - A\) with \(r_1 + r_2 = A\).
The deviation is minimum when the ray passes symmetrically through the prism, that is \(i = e\) and \(r_1 = r_2 = A/2\).
(A) Incident and emergent rays are symmetric about the prism: true.
(B) With \(r_1 = r_2\), the ray inside the prism makes equal angles with the two faces, so it is parallel to the base: true.
(C) Angle of incidence equals angle of emergence: true.
(D) Emergence angle double the incidence angle contradicts \(i = e\): false.
So statements (A), (B) and (C) are true.
Answer: (3) Statements (A), (B) and (C) are true