The angles of incidence and refraction when light travels from one medium to another can be calculated using Snell’s Law.

Deﬁnition: Snell’s Law

n_{1}sin θ_{1} = n_{2} sin θ_{}_{2}_{}_{}where

n

_{1 }= Refractive index of material 1

n

_{2 }= Refractive index of material 2

θ

_{1 }= Angle of incidence

θ

_{2 }= Angle of refraction

If

n_{2 }<>1then from Snell’s Law,

sin

θ1 < style="font-style: italic;">θ2.

For angles smaller than 90◦, sin

θ increases as

θ increases. Therefore,

θ1 < θ2.This means that the angle of incidence is less than the angle of refraction and the light ray is

away toward the normal.

Similarly,if

n_{2} > n_{1}then from Snell’s Law,

sin θ1 > sin θ2.For angles smaller than 90◦, sin

θ increases as

θ increases. Therefore,

θ1 > θ2.This means that the angle of incidence is greater than the angle of refraction and the light ray is

bent toward the normal.What happens to a ray that lies along the normal line?Worked Example : Using Snell’s Law

Question:

A light ray with an angle of incidence of 35◦ passes from water to air.

Find the angle of refraction using Snell’s Law . Discuss the meaning of your answer.

(the refractive index is 1,333 for water and about 1 for air)

Answer

According to Snell’s Law: n_{1}sin θ_{1} = n_{2} sin θ_{}_{2} 1.33 sin 35◦ = 1 sin θ_{2} sin θ_{2} = 0.763 θ_{2 }= 49.7◦ The light ray passes from a medium of high refractive index to one of low refractive index. Therefore, the light ray is bent away from the normal.Test your understanding :

1. A light ray passes from water to diamond with an angle of incidence of 75◦. Calculate the angle of refraction. Discuss the meaning of your answer.

(Answer: 32.1◦, ....bent towards the normal)