Question

The figure shows a ray incident at angle $i=\frac{\pi }{3}$. If the plot drawn show the variation of | r-i | versus $\frac{{\mu }_1}{{\mu }_2}=k$, (r = angle of refraction)

• A. the value of $k_{1}is\frac{2}{\sqrt{3}}$
• B. the value of ${\theta }_1=\frac{\pi }{6}$
• C. the value of ${\theta }_2=\frac{\pi }{3}$
• D. the value of $k_2$ is 1.

Answer 1

The correct option is D the value of $k_2$ is 1.

(D) If k = 1 the ${\mu }_1={\mu }_2$
$\therefore$ i = r
i - r = 0
$k_2=1$
(C) If k is very large then ${\mu }_1>>{\mu }_2$. Therefore the refractive ray medium ${\mu }_1$ is high.
So $r\to 0\therefore |r-i|=i={\theta }_2\therefore {\theta }_2=\frac{\pi }{3}$
(B) If k is smaller than 1. Then TIR occurs
$\therefore {\theta }_1=|r-i|=|90-60|={30}^o\therefore$
${\theta }_1=\frac{\pi }{6}$