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A ray of light strikes a glass plate at an angle of $60^{\circ}$. If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is
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1547 Upvotes
Verified Answer
The correct answer is:
$\sqrt{3}$
Here, angle of incidence is $60^{\circ}$
$$
\mu=\frac{\sin i}{\sin r}
$$
$\sin i=\mu \sin r$
here,
$$
\begin{aligned}
r &=90-i \\
\sin i &=\mu \sin \left(90^{\circ}-i\right)=\mu \cos i \\
\mu &=\frac{\sin i}{\cos i}=\tan i=\tan 60^{\circ} \\
\mu &=\sqrt{3}
\end{aligned}
$$
$$
\mu=\frac{\sin i}{\sin r}
$$
$\sin i=\mu \sin r$
here,
$$
\begin{aligned}
r &=90-i \\
\sin i &=\mu \sin \left(90^{\circ}-i\right)=\mu \cos i \\
\mu &=\frac{\sin i}{\cos i}=\tan i=\tan 60^{\circ} \\
\mu &=\sqrt{3}
\end{aligned}
$$
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