Three beams of blue, green and orange colour are made to pass separately through a prism . In the position of minimum deviation, the angle of refraction will be (the angle of prism is $60^\circ$)

In the position of minimum deviation, the angle of refraction at the first face is equal to the angle of incidence at the second face, so $r_1 = r_2 = r$.

The angle of the prism is related to the angles of refraction by $A = r_1 + r_2 = 2r$.

Therefore, the angle of refraction is $r = \dfrac{A}{2}$.

Given the angle of the prism $A = 60^\circ$, we get $r = \dfrac{60^\circ}{2} = 30^\circ$.

This relation is purely geometric and depends only on the angle of the prism. It is independent of the refractive index of the material and the wavelength of the light.

Thus, the angle of refraction will be $30^\circ$ for blue, green, and orange colors when each is at its respective position of minimum deviation.

Answer: $30^\circ$ for blue , green and orange colour