Question

How do you verify experimentally that the angle of refraction is more than the angle of incidence when light rays travel from a denser to a rarer medium?

Answer 1

Hint : When the light travels from one medium to another medium the velocity of light changes and the light bends. This bending of light is referred to as refraction. The amount of increase or decrease in the velocity depends on the medium through which light travels. Light has a greater speed when it enters an optically rarer medium than a denser one and will bend towards the normal when it travels from a rarer medium to a denser one.

Complete step by step answer.
Step 1: Describe the experimental setup for the refraction of light from a denser medium to a rarer medium.
To determine whether the angle of refraction is more than or less than the angle of incidence when light travels from a denser to a rarer medium, we consider an air-glass-air interface.
Air will be the rarer medium and a rectangular glass slab will be the denser medium.
First, the glass slab is placed on a piece of paper and its outline is drawn on the paper so that even if the glass slab somehow moves from its position during the observation it can be brought back to its original position. A laser source will be placed such that light rays from the source are incident on one side of the glass slab at a known angle say ${\theta _i}$ and it is called the angle of incidence. A point is marked on the paper corresponding to the incident light from the laser source. We will see the refracted laser light coming out of the other side of the slab and we mark a point on the paper indicating this refracted ray.
Now the glass slab is removed from the paper. Lines are drawn corresponding to the marked points on the paper to the rectangular outline of the slab. A line passing through the rectangle and connecting the other two lines is also drawn. Now the angles made by each line at the upper and lower side of the rectangle are measured using a protractor. The figure given below depicts these markings on the paper.

In the above figure, AB is the incident light, BC is the refracted ray at the first boundary (air-glass), CD is the refracted ray at the second boundary (glass-air). NM and PQ represent the normals to the boundaries. Also, ${\theta _i} = i$ is the angle of incidence, ${\theta _r} = {r_1}$ is the angle of refraction for the first boundary and ${\theta _r} = {r_2}$ is the angle of refraction for the second boundary.
Step 2: Describe the bending of light from the laser source at the two interfaces.
As the laser light gets incident on the first interface being the air-glass interface, it will undergo refraction and bend towards the normal as the speed of light decreases when it travels from the rarer medium of air to the denser medium of glass. Here we have $i > {r_1}$ .
Now, this ray of light travels in a straight line and gets incident on the second interface being the glass-air interface. The light again refracts at the boundary but this time bends away from the normal. This is because the speed of light decreases when it travels from the denser medium of glass to the rarer medium of air. Here we have ${r_1} < {r_2}$ .
Step 3: Based on the bending of light at the two interfaces conclude the observations.
At the air-glass interface, light bent towards the normal and so the angle of refraction will be smaller than the angle of incidence for this interface.
But for the glass-air interface or the denser-rarer interface, the light bent away from the normal. This suggests that the angle of refraction is greater than the angle of incidence for this interface.
Our observations of the experiment will corroborate this theory. And hence we conclude that when light enters from a denser to a rarer medium, the angle of refraction will be more.

Note: At the second interface, its angle of incidence will be the angle of refraction at the first boundary i.e., ${\theta _i} = {r_1}$ . The light in a denser medium encounters more matter and so scattering will be more and the speed of light will thus decrease whereas in a rarer medium, the lesser amount of matter present scatters less light and thus speed will be more.