Question

A prism of refractive index $\sqrt{2}$ has a reflecting angle of ${60}^0$. At what angle must a ray be incident on it so that it suffers minimum deviation?

• A. $i={45}^0$
• B. $i={60}^0$
• C. $i={30}^0$
• D. $i={90}^0$

Answer 1

The correct option is A $i={45}^0$

For minimum deviation, $r_1=r_2$

From triangle, $r_1+r_2+120=180$

$r_1+r_2=60\Rightarrow r_1=r_2={30}^o$

Now using snail law:

$1sin\left(i_1\right)=\sqrt{2}sin\left(r_1\right)$

$sin\left(i_1\right)=\frac{1}{\sqrt{2}}\Rightarrow i_1={45}^o$