Question

In the following ray diagrams, a ray of light is incident at an equal angle of incidence at the interface of four different materials. Which material is optically densest?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

We know that the material having the greatest value of refractive index is optically densest.

Also, refractive index of any material with respect to air,
$\mu =\frac{\sin i}{\sin r}$

Here, $i=$ constant

$\Rightarrow \mu \propto \frac{1}{\sin r}........\left(1\right)$

For angle less than ${90}^{\circ }$, value of $\sin \theta$ is lower for lower value of angle.

Thus, $\sin {15}^{\circ }<\sin {25}^{\circ }<\sin {45}^{\circ }<\sin {60}^{\circ }$

So, from eq.(1)
${\mu }_A>{\mu }_C>{\mu }_B>{\mu }_D$

Hence, material $-A$ is the densest material.

Alternative solution:

Lesser the speed of light in the given medium more it bends towards the normal. Or the angle of refraction is small. So, the diagram provided in option (a) depicts the refracted ray with a smaller angle of refraction comapred to other options.