# Question Video: Refraction Angle of a Light Ray

The path of a light beam in air goes from an angle of incidence of 35.0Β° to an angle of refraction of 22.0Β° when it enters a rectangular block of plastic. What is the index of refraction of the plastic?

02:20

### Video Transcript

The path of a light beam in air goes from an angle of incidence of 35.0 degrees to an angle of refraction of 22.0 degrees when it enters a rectangular block of plastic. What is the index of refraction of the plastic?

We can highlight the angle of incidence, 35.0 degrees, and refer to that as π sub π. Likewise the angle of refraction, 22.0 degrees, we can refer to as π sub π. We want to know the index of refraction of the plastic, which weβll call π sub π. Letβs begin our solution by drawing a diagram of the situation.

When a ray of light crosses the air and plastic interface, the ray is refracted based on the index of refraction of the plastic. Weβll assume that the index of refraction of air, π sub π, is equal to 1.00. To solve for the index of refraction of the plastic block, we can recall Snellβs law which says that when light crosses an interface moving from a material with index of refraction π sub one to one with index of refraction π sub two, then π one times the sine of the incident angle equals π two times the sine of the refracted angle.

Applying Snellβs law to our particular situation, we have π sub π, the index of refraction of air, times the sine of the incident angle 35.0 degrees equals π sub π, the index of refraction of the plastic, times the sine of the refracted angle π sub π.

Dividing both sides by the sine of π sub π, π sub π equals π sub π times the sine of π sub π divided by the sine of π sub π. We can now plug in for π sub π, π sub π, and π sub π. When we enter these values on our calculator, we find that, to three significant figures, π sub π is 1.53. Thatβs the index of refraction of the block of plastic.