Question

A ray of light is incident on a prism $ABC(AB=BC)$ & travels as shown. The refractive index of the prism material should be at least

• A. $\frac{4}{3}$
• B. $\sqrt{2}$
• C. $1.5$
• D. $\sqrt{3}$

Answer 1

The correct option is B $\sqrt{2}$


From the diagram, $i={45}^{\circ }$

We can observe that total internal reflection is taking place at surface $AB$ and $BC$. TIR takes place when incident angle is greater than the critical angle.

Thus, $i>i_c$

$\Rightarrow$ ${45}^{\circ }$$\ge i_c$ ____(1)

At both the surfaces incident angle is ${45}^{\circ }$. So, above condition will hold true at both the surfaces.

Critical angle $\left(i_c\right)$ for the prism:

$\Rightarrow$ $\sin i_c=\frac{1}{{\mu }_p}$ ______(2)

Where ${\mu }_p$ is refractive index of prism material.

Using equation $1\text{and}2$:

$\sin {45}^{\circ }>\sin i_c$

$\Rightarrow \frac{1}{\sqrt{2}}>\frac{1}{{\mu }_p}$

$\therefore {\mu }_p>\sqrt{2}$