The refractive index of the material of an equilateral prism is \( \sqrt{2} \). The angle of minimum deviation of that prism is _____________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 30^\circ \)
At minimum deviation the refractive index of a prism of angle \( A \) is given by the prism formula
\( \displaystyle \mu = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \)
For an equilateral prism \( A = 60^\circ \), so \( \sin(A/2) = \sin 30^\circ = 1/2 \):
\( \displaystyle \sin\left(\frac{60^\circ + D_m}{2}\right) = \sqrt{2} \times \frac{1}{2} = \frac{1}{\sqrt{2}} \)
\( \displaystyle \frac{60^\circ + D_m}{2} = 45^\circ \;\Rightarrow\; D_m = 30^\circ \)