The refractive index of a transparent liquid filled in an equilateral hollow prism is $$\sqrt{2}$$. The angle of minimum deviation for the liquid will be _____°.

For an equilateral prism ($$A = 60°$$), the refractive index and angle of minimum deviation are related by:

$$n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$

$$\sqrt{2} = \frac{\sin\left(\frac{60° + D_m}{2}\right)}{\sin 30°} = \frac{\sin\left(\frac{60° + D_m}{2}\right)}{0.5}$$

$$\sin\left(\frac{60° + D_m}{2}\right) = \frac{\sqrt{2}}{2} = \sin 45°$$

$$\frac{60° + D_m}{2} = 45°$$

$$60° + D_m = 90°$$

$$D_m = 30°$$

The angle of minimum deviation is $$\mathbf{30}$$°.