Question Video: Calculating the Angle of Refraction of a Light Ray Physics • Second Year of Secondary School

Video Transcript

A light ray traveling in air is incident on the flat surface of a plastic block with a refractive index of 1.5, hitting the surface at an angle of 45 degrees from the line normal to it. At what angle from the line normal to the surface does the refracted ray in the block travel? Answer to the nearest degree.

This is a question about light refracting as it travels from air into a plastic block. Remember that refraction is the change in direction of a light ray as it passes from one medium to another. This occurs because light travels at different speeds in different media.

We can see this in everyday life if we put a pencil in a glass of water. The pencil appears to change shape; it is no longer straight. However, the pencil has not been bent. Instead, different parts of the pencil are now in different media. Some of it is in the water, and some of it is in the air. Water is a different medium to air, and so light changes its speed as it travels between them. This causes the light to change direction, which is why the pencil appears to be bent.

The exact same concepts apply when light reaches the plastic block we’re asked about in this question. We see that the light travels in the air until it reaches the plastic block and changes direction.

We can talk about this change in direction in terms of the angle of incidence of the initial light ray, and the angle of refraction of the refracted ray. When we talk about angles of refracting light, we measure them from the line normal to the surface where refraction occurs. Normal to the surface just means perpendicular to the surface.

We can now label two angles in our diagram. One is the angle of incidence, the angle at which the incident light hits the surface of the plastic block. And the other is the angle of refraction, the angle the light travels after it has been refracted.

We are told the angle of incidence is 45 degrees. We are also told the refractive index of the plastic block. Remember that the refractive index is a property of a material that is a measure of how fast light travels through it. It has no units, and the larger its value, the slower light will travel through the medium. The smaller its value, the faster light will travel through the medium. In air, we can approximate the refractive index as one.

The relationship between the angles and the refractive indices is given by Snell’s law. 𝑛 sub 𝑖 times the sin of 𝜃 sub 𝑖 equals 𝑛 sub 𝑟 times the sin of 𝜃 sub 𝑟, where 𝑛 sub 𝑖 is the refractive index of the light ray’s initial material. 𝑛 sub 𝑟 is the refractive index of the light ray’s final material. 𝜃 sub 𝑖 is the angle of incidence. And 𝜃 sub 𝑟 is the angle of refraction. The question is asking us for 𝜃 sub 𝑟, the angle of refraction, so we need to rearrange this equation to make 𝜃 sub 𝑟 the subject.

First, we divide both sides by 𝑛 sub 𝑟, canceling that factor on the right. Then, we take the inverse sine of both sides in order to isolate 𝜃 sub 𝑟. This can also be written as 𝜃 sub 𝑟 equals the inverse sin of 𝑛 sub 𝑖 times the sin of 𝜃 sub 𝑖 divided by 𝑛 sub 𝑟.

Substituting our values in, we have 𝑛 sub 𝑖 equals one for air, 𝑛 sub 𝑟 equals 1.5 for the plastic block, and 𝜃 sub 𝑖 equals 45 degrees. When we calculate 𝜃 sub 𝑟, we get an angle of 28.125 and so on degrees. The question asks for the angle of refraction to be given to the nearest degree, so our final answer is 𝜃 sub 𝑟 equals 28 degrees.

The angle of refraction of the ray of light is 28 degrees.