Question

Ask Your Teacher A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 33.5° and the angle of refraction is 19.3°, find the critical angle for the liquid when surrounded by air.

Answer 1

Answer:

The critical angle for the liquid when surrounded by air is 30 degrees.      

Explanation:

Given that,

The angle of incidence is 33.5° and the angle of refraction is 19.3°. Firstly, we can find the refractive index of the liquid. It can be calculated using Snell's law as :

$n=\dfrac{\sin i}{\sin r}\\\\n=\dfrac{\sin (33.5)}{\sin (19.3)}\\\\n=2$

The critical angle is given by :

$\theta_c=\sin^{-1}(\dfrac{n_1}{n_2})$

Here, $n_1$ is refractive index of air and $n_2$ is refractive index of liquid.

$\theta_c=\sin^{-1}(\dfrac{1}{2})\\\\\theta_c=30^{\circ}$

So, the critical angle for the liquid when surrounded by air is 30 degrees.