Which of the following statements are true for the minimum deviation…

The correct answer is Option (2) → (A), (B) and (C) only

At minimum deviation the ray passes through the prism symmetrically: the angle of incidence equals the angle of emergence and the two refraction angles inside are equal.

    \( i = e \)
    \( r_1 = r_2 = r \)

    \( \displaystyle r_1 + r_2 = A \;\Rightarrow\; A = 2r \)

(A) The angle of the prism is twice the angle of refraction. — Correct. With \( r_1 = r_2 = r \), the relation \( r_1 + r_2 = A \) gives \( A = 2r \).

(B) The refracted ray is parallel to the base of prism. — Correct. Because the path is symmetric, the ray inside the (usual isosceles) prism travels parallel to the base.

(C) The angle of incidence is equal to the angle of emergence. — Correct. This is the defining condition \( i = e \) of minimum deviation.

(D) The angle of deviation is half the angle of a prism. — Incorrect. The minimum deviation is \( \delta_m = 2i - A \); it depends on the refractive index and is not fixed at \( A/2 \).

NCERT (2026-27):
Refraction Through a Prism – “… At the minimum deviation D_m, the refracted ray inside the prism becomes parallel to its base. We have δ = D_m, i = e which implies r₁ = r₂. Equation (9.34) gives

    \( \displaystyle 2r = A \quad \text{or} \quad r = \frac{A}{2} \qquad (9.36) \)

In the same way, Eq. (9.35) gives

    \( \displaystyle D_m = 2i - A, \quad \text{or} \quad i = \frac{A + D_m}{2} \qquad (9.37) \)”