Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.

Choose the correct answer from the options given below.

For a prism of refracting angle $$A$$ made of material having refractive index $$n$$, when the deviation is minimum the ray of light follows a symmetrical path.

Conditions at minimum deviation:
(i) Angle of incidence $$i_1$$ equals angle of emergence $$i_2$$.
(ii) Angle of refraction at first surface $$r_1$$ equals angle of refraction at second surface $$r_2$$, say $$r$$.
(iii) From the geometry of the prism, $$r_1 + r_2 = A$$, therefore at minimum deviation $$2r = A \Rightarrow r = \dfrac{A}{2}$$.

The deviation-incidence graph is a U-shaped curve with its lowest point at the minimum deviation $$D_m$$. Using Snell’s law at minimum deviation one writes

$$n = \dfrac{\sin\left(\dfrac{A + D_m}{2}\right)}{\sin\left(\dfrac{A}{2}\right)}$$ $$-(1)$$

Now each statement can be checked one by one.

Statement A: “The refracted ray inside prism becomes parallel to the base.”
In the isosceles triangle formed by the two refracting faces and the base, the internal ray makes the angle $$r = A/2$$ with each face. Hence it is parallel to the side opposite the apex, i.e. the base. So Statement A is TRUE.

Statement B: “Larger angle prisms provide smaller angle of minimum deviation.”
From equation $$(1)$$, keeping $$n$$ fixed, increase in $$A$$ increases the numerator $$\sin\bigl(\tfrac{A+D_m}{2}\bigr)$$ as well as the denominator $$\sin\bigl(\tfrac{A}{2}\bigr)$$, but the net result is that $$D_m$$ rises with $$A$$. A quick numerical check with $$n = 1.50$$ gives
for $$A = 30^\circ,\; D_m \approx 15.7^\circ$$;
for $$A = 60^\circ,\; D_m \approx 37.2^\circ$$.
Thus larger $$A$$ leads to larger, not smaller, $$D_m$$. So Statement B is FALSE.

Statement C: “Angle of incidence and angle of emergence become equal.”
This is the defining condition of minimum deviation (symmetrical path). Hence Statement C is TRUE.

Statement D: “There are always two sets of angle of incidence for which deviation will be the same except at minimum deviation setting.”
Because the deviation curve is symmetric about the minimum, every value of deviation greater than $$D_m$$ is obtained for two equal and opposite departures of $$i$$ from the symmetry point. Therefore Statement D is TRUE.

Statement E: “Angle of refraction becomes double of prism angle.”
We have already derived $$r = \dfrac{A}{2}$$, not $$2A$$. Hence Statement E is FALSE.

The TRUE statements are A, C, and D only.

Correct choice: Option A (A, C and D Only).