Question

Prove the following statements.
a. If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that, i = e.
b. A raibow is the combined effect of the refraction, dispersion, and total internal reflection of light.

Answer 1

a.

Let $\mu$ be the refractive index of the glass slab. Then, according to Snell's law,
$\frac{\sin i}{\sin r_1}=\mu$ .....(i)
and
$\frac{\sin r_2}{\sin e}=\frac{1}{\mu }$ .....(ii)
But, r₁ = r₂ .....(iii)
Putting (iii) in (i), we have
$\frac{\sin i}{\sin r_2}=\mu$ .....(iv)
Multiplying (i) and (iv), we have
$$\begin{gathered} \frac{\sin i}{\sin e}=1 \\ \mathrm{or} \\ i=e \end{gathered}$$

b.

After rainfall, the tiny droplets of water present in the atmosphere act as a prism for the rays coming from the Sun. Thus, the sunlight after striking the surface of the droplets gets refracted and dispersed into its seven components as shown in the figure (figure showing just two components). After this, the light rays are subjected to total internal reflection. Then the rays are again refracted when they come out of the water droplet. Hence, rainbow formation is the combined effect of the refraction, dispersion, and total internal reflection of light.