Question

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

Choose the correct option.

• A. the value of $k_1$ is $\frac{2}{\sqrt{3}}$
• B. the value of ${\theta }_1=\pi /6$
• C. the value of ${\theta }_2=\pi /3$
• D. the value of $k_2$ is 1
• E. the value of $k_1$ is 1
  

Answer 1

Answer: (C), (D)

The correct options are
C the value of ${\theta }_2=\pi /3$
D the value of $k_2$ is 1

Using Snell's law : ${\mu }_2$ $sini={\mu }_1$ $sinr$

$\therefore$ $\frac{{\mu }_2}{{\mu }_1}$ $sin\left(\pi /3\right)=$ $sinr$

$⟹$ $sinr=\frac{\sqrt{3}}{2k}$

Putting $k=1$

$\therefore$ $sinr=\frac{\sqrt{3}}{2\times 1}$ $⟹r=\pi /3$ or $2\pi /3$

Using $r=2\pi /3$ $⟹|r-i|=|2\pi /3-\pi /3|=\pi /3$

Thus ${\theta }_2=\pi /3$

Hence, correct options are C and D.