A ray of light travels from a medium of refractive index 2 to another medium of refractive index…
A ray of light travels from a medium of refractive index 2 to another medium of refractive index \(\sqrt{2}\). Total internal reflection takes place when the angle of incidence is
\(30^{\circ}\)
\(45^{\circ}\)
\(60^{\circ}\)
\(80^{\circ}\)
Solution
Refractive index of first medium,
\(\mu_1=2\)
Refractive index of second medium,
\(\mu_2=\sqrt{2}\)
If \(i_C\) be the angle of incidence in the case of total internal reflection, then
$\begin{aligned}
& \mu_1^2=\frac{1}{\sin i_C} \Rightarrow \frac{\mu_1}{\mu_2}=\frac{1}{\sin i_C} \\
& \Rightarrow \frac{2}{\sqrt{2}}=\frac{1}{\sin i_C} \Rightarrow \sqrt{2}=\frac{1}{\sin i_C} \\
& \Rightarrow \sin i_C=\frac{1}{\sqrt{2}} \Rightarrow \sin i_C=\sin 45^{\circ} \\
& \Rightarrow i_C=45^{\circ}
\end{aligned}$