Question

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid point of one end of the rod as shown in the figure.
The incident angle $\theta$ for which the light ray grazes along the wall of the rod is

• A. $si{n}^{-1}\left(\frac{1}{2}\right)$
• B. $si{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$
• C. $si{n}^{-1}\left(\frac{2}{\sqrt{3}}\right)$
• D. $si{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Answer 1

Answer: (D)

$sinC=\frac{\sqrt{3}}{2}.....\left(1\right)$
$Sinr=sin\left(90-C\right)=cosC=\frac{1}{2}$
$\frac{sin\theta }{sinr}=\frac{{\mu }_2}{{\mu }_1}$
$sin\theta =\frac{2}{\sqrt{3}}\times \frac{1}{2}$
$\theta =si{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$