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A ray of light is incident at an angle $i$ on a glass slab of refractive index $\mu$. The angla between reflected and refracted light is $90^{\circ}$ Then, the relationship between $i$ and $\mu$ is
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Verified Answer
The correct answer is:
$\tan i=\mu$
As situation can be diagrammatically as below
From law of reflection
$$
i=\theta
$$
Now, $\quad \theta+r+90^{\circ}=180^{\circ}$
$$
\begin{aligned}
\Rightarrow \quad i+r+90^{\circ} &=180^{\circ} \\
r &=90^{\circ}-i
\end{aligned}
$$
Also, from Snell's law $\frac{\sin i}{\sin r}=\mu \Rightarrow \frac{\sin i}{\sin \left(90^{\circ}-i\right)}=\frac{\sin i}{\cos i}=\mu$
$\Rightarrow \tan i=\mu$
From law of reflection
$$
i=\theta
$$
Now, $\quad \theta+r+90^{\circ}=180^{\circ}$
$$
\begin{aligned}
\Rightarrow \quad i+r+90^{\circ} &=180^{\circ} \\
r &=90^{\circ}-i
\end{aligned}
$$
Also, from Snell's law $\frac{\sin i}{\sin r}=\mu \Rightarrow \frac{\sin i}{\sin \left(90^{\circ}-i\right)}=\frac{\sin i}{\cos i}=\mu$
$\Rightarrow \tan i=\mu$
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