Question

# A ray of light travelling in a transparent medium falls on a surface separating the medium from air, at an angle of incidence of ${{45}^{o}}$. The ray undergoes total internal reflection. If $n$is the refractive index of the medium with respect to air, select the possible values of $n$ from the followinga)$1.3$b)$1.4$c)$1.5$d)$1.2$

Hint: The angle of incidence is given in the question, so, substitute the value in the total internal reflection formula. The value of the refractive index of air is one. For total internal refraction to occur, the angle of incidence must exceed the critical angle.

Formula used:
$i>{{\sin }^{-1}}(\dfrac{1}{\mu })$

For total internal reflection to occur, the angle of incidence must be greater than the critical angle.
Let the refractive index be assumed as $\mu$and the angle of incidence as $i$,
The critical angle is calculated as,
${{\sin }^{-1}}(\dfrac{1}{\mu })$
Therefore, the formula turns into,
\begin{align} & i > {{\sin }^{-1}}(\dfrac{1}{\mu }) \\ & \sin (i) > \dfrac{1}{\mu } \\ & \sin ({{45}^{0}}) > \dfrac{1}{\mu } \\ & \mu > \sqrt{2} \\ & \mu > 1.44 \\ & \\ \end{align}

So, the correct answer is “Option C”.