An equilateral prism is made of material of refractive index \( \sqrt{3} \). Angle of minimum deviation through the prism is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 60^\circ \)
At minimum deviation the refractive index of a prism is given by the prism formula
\( \displaystyle n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \)
For an equilateral prism \( A = 60^\circ \) and here \( n = \sqrt{3} \).
\( \displaystyle \sin\left(\frac{60^\circ + D_m}{2}\right) = \sqrt{3}\,\sin 30^\circ = \frac{\sqrt{3}}{2} \)
\( \displaystyle \frac{60^\circ + D_m}{2} = 60^\circ \;\Rightarrow\; D_m = 60^\circ \)