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
$ \mu = \frac{sin\frac{A+D_m}{2}}{sin\frac{A}{2}} $
$ A = 60^o$
$\Rightarrow \sqrt{2}= \frac{sin(\frac{60^o+D_m}{2}}{sin30^o}= 2 sin(\frac{60^o+D_m}{2} $
$\Rightarrow sin(\frac{60^o+D_m}{2} = \frac{1}{\sqrt{2}} = sin 45^o$
$ \frac{60^o+D_m}{2} = 45^o \Rightarrow D_m = 30^o$
The correct answer is Option (3) → 30°