1. Use the prism condition at minimum deviation

For a prism of angle $A$, in the position of minimum deviation, the path is symmetric. Hence,

$r_1 = r_2 = r$

and

$r_1 + r_2 = A$

So,

$2r = A \implies r = \frac{A}{2}$

2. Substitute the given prism angle

Given:

$A = 60^\circ$

Therefore,

$r = \frac{60^\circ}{2} = 30^\circ$

3. Check dependence on colour

Although red and violet light have different refractive indices and hence different minimum deviations, the internal angles of refraction at minimum deviation depend only on the prism angle through

$r = \frac{A}{2}$

So for both red and violet,

$r = 30^\circ$

4. Evaluate the options

• A: $30^\circ$ for both the colours — Correct
• B: greater for the violet colour — Incorrect
• C: greater for the red colour — Incorrect
• D: equal but not $30^\circ$ for both the colours — Incorrect

Therefore, the correct option is A.