Snell’s law and the critical angle

Physics terms• critical angle

• total internal reflection

EquationsThe index of refraction of the first material times the sine of the angle of incidence equals the index of refraction of the second material times the sine of the angle of refraction.

The sine of the critical angle is the ratio of the indices of refraction of the two materials.

What factors do you think it depends on?

?

Finding the refracted ray

When light rays refract, how can we know what the angle of refraction will be?

The refracted angle depends on: •the angle of incidence•the index of refraction of each material

The angle of refraction can be calculated using Snell’s law.

Snell’s law

ni = index of refraction of 1st material

nr = index of refraction of 2nd material

θi = angle of incidence

θr = angle of refraction

sin is the sine function

Snell’s law

The sine function is simply a ratio of two sides of a right triangle:

This angle of incidence is 30º.

The hypotenuse is twice as long as the opposite side.

sin 30º = ½ = 0.5

opposite side

hypotenuse

What is the sine function?

30o

The index of refractionA light beam in air strikes an unknown material with an angle of incidence of 60°, resulting in an angle of refraction of 20.5°.

What is the unknown material's index of refraction?

n = 2.42 What material is this?

Light passing from low to high index of refraction bends

towards the normal.

Light passing from high to low index of refraction bends

away from the normal.

Direction of refraction (review)

Light passing from high to low index of refraction bends away from the normal and toward the boundary.

As the angle of incidence increases, the amount of bending increases . . .

and the refracted ray moves even closer to the boundary.

Direction of refraction

The critical angleLight passing from high to low index of refraction (ni > nr) bends away from the normal.

As the angle of incidence increases, the angle of refraction approaches 90º.

The critical angleLight passing from high to low index of refraction (ni > nr) bends away from the normal.

As the angle of incidence increases, the angle of refraction approaches 90º.

The critical angle is the angle of incidence that results in an angle of refraction of 90º.

What do you think happens if you exceed the critical angle?

The critical angleLight passing from high to low index of refraction (ni > nr) bends away from the normal.

As the angle of incidence increases, the angle of refraction approaches 90º.

The critical angle is the angle of incidence that results in an angle of refraction of 90º.

If you exceed the critical angle the refracted ray disappears.

The result: total internal reflection.

Total internal reflection

Total internal reflection

This can ONLY happen if the incident material has the higher index of refraction.

If you exceed the critical angle the refracted ray disappears.

The result: total internal reflection.