Snell’s Law

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
n₁sin θ₁ = n₂ sin θ₂
where
n₁ = Refractive index of material 1
n₂ = Refractive index of material 2
θ₁ = Angle of incidence
θ₂ = Angle of refraction

Remember that angles of incidence and refraction are measured from the normal, which is an imaginary line perpendicular to the surface.
If
n₂ <>1
then 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
n₂ > n₁
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: n₁sin θ₁ = n₂ sin θ₂ 1.33 sin 35◦ = 1 sin θ₂ sin θ₂ = 0.763 θ₂ = 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)