Question

A light ray falling at an angle of 45° with the surface of a clean slab of ice of thickness 1.00 m is refracted into it at an angle of 30°. Calculate the time taken by the light rays to cross the slab. Speed of light in vacuum = 3 × 10⁸ m s⁻¹.

Answer 1

Given,
Angle of incidence, i = 45°
Angle of refraction, r = 30°
Using Snell's law,
$\frac{\sin i}{\sin r}=\frac{3\times {10}^8}{v}$
$=\frac{\sin 45°}{\sin 30°}=\frac{\left({\displaystyle \frac{1}{\sqrt{2}}}\right)}{\left({\displaystyle \frac{1}{2}}\right)}$
$=\frac{2}{\sqrt{2}}=\sqrt{2}$
$$\begin{gathered} \mathrm{So}, \\ v=\frac{3\times {10}^8}{\sqrt{2}}\mathrm{m}/s \end{gathered}$$

Let x be the distance travelled by light in the slab.
Now,
$x=\frac{1\mathrm{m}}{\cos 30°}=\frac{2}{\sqrt{3}}\mathrm{m}$
We know:
Time taken $=\frac{\mathrm{Distance}}{\mathrm{Speed}}$
$=\frac{2}{\sqrt{3}}\times \frac{\sqrt{2}}{3\times {10}^8}$
= 0.54 × 10⁻⁸
= 5.4 × 10⁻⁹ s