A light ray is incident at an angle $i=\pi /3$  at the plane boundary separating two media. The light passes from medium 1 to medium 2. Figure. shows a plot drawn showing the variation of  $|r-i|$ versus $\frac{{\mu }_2}{{\mu }_1}=C$. Here $r$ is the angle of refraction and  ${\mu }_1,{\mu }_2$ the refractive indices of medium 1 and 2 respectively. Which of the following are correct?

Keeping the first medium fixed (i.e., ${\mu }_1=const.$) and $i={60}^{\circ }$ (given), let us analyses the situation when ${\mu }_2$  is varied and hence, $C=\frac{{\mu }_2}{{\mu }_1}$ also gets varied.

Initially when  $C>1$
i.e., when   ${\mu }_2<{\mu }_1$
Since $\mu \ge 1$       
 $\therefore$  ${\mu }_{\min }=1$     
  $\therefore C=\frac{{\mu }_2}{{\mu }_1}$

$\Rightarrow C_1=\frac{1}{{\mu }_1}$

From Snell’s law,   $\frac{\sin {60}^{\circ }}{\sin {90}^{\circ }}=\frac{1}{{\mu }_1}=C_1=\sqrt{3}/2$

At any instant i.e., when   $i={60}^{\circ },r={90}^{\circ }$
$|i-r|={30}^{\circ }=\pi /6$ 
When C is increased indefinitely i.e., when ${\mu }_2>>{\mu }_1$
$\frac{\sin i}{\sin r}>>1$

or  $\sin r\to 0$

or  $r\to 0$

In that Situation,  $\beta =|i-r|$
        $$\begin{gathered} =|{60}^{\circ }-0| \\ =\pi /3 \end{gathered}$$             
When  ${\mu }_2={\mu }_1,$ i.e., When C = 1
$I = r$ and hence  $|i-r|=0$
$\therefore$ The point $C_2$ corresponds to $C = 1$ at zero deflection.