Angle of Refraction for Red and Violet Light at Minimum Deviation

To determine the angle of refraction for red and violet light at the position of minimum deviation, we use the standard refraction relations for a prism.

For a prism with an angle of prism $A$, the angles of refraction at the first and second surfaces, $r_1$ and $r_2$, satisfy the relation:
$r_1 + r_2 = A$

At the condition of minimum deviation ($\delta = \delta_{\text{min}}$):

1. The ray of light passes symmetrically through the prism.
2. The angle of incidence equals the angle of emergence, i.e., $i = e$.
3. The angles of refraction at the two faces become equal, i.e., $r_1 = r_2 = r$.

Substituting this condition into the relation:
$r + r = A \implies 2r = A$
$r = \frac{A}{2}$

Given that the angle of the prism is $A = 60^\circ$:
$r = \frac{60^\circ}{2} = 30^\circ$

The value of $r$ depends solely on the angle of the prism $A$ and is independent of the refractive index of the prism material or the wavelength (colour) of the incident light.

Therefore, in the position of minimum deviation, the angle of refraction is $30^\circ$ for both red and violet colours.

Correct Option: (A)