An Introduction to Refraction

SNC2D

Index of Refraction

Light will travel more slowly in more dense materials. The ratio of the speed of light in a vacuum (or air) to the speed in the material is the index of refraction (or refractive index), n.

nc

v

Index of Refraction: Example

For water, the index of refraction is 1.33. The speed of light in water is therefore:

?:

100.3

33.1:8

vR

c

nG

sm

Index of Refraction: Example

For water, the index of refraction is 1.33. The speed of light in water is therefore:

n

cv

v

cnA :

?:

100.3

33.1:8

vU

c

nG

sm

Index of Refraction: Example

For water, the index of refraction is 1.33. The speed of light in water is therefore:

sms

m

vS

n

cv

v

cnS

88

103.233.1

100.3:

:

?:

100.3

33.1:8

vU

c

nG

sm

Frequency and Wavelength

Since the wave slows down but the frequency remains the same (the frequency of a wave is always the frequency of the source), the wavelength gets shorter. f

vfv

Boundaries

So in 2D (with the boundary at an angle to the wave), the wave will bend as those parts that enter the more-dense material first slow down first.

(The black lines show the crests or “wavefronts”).

Please Note!

If the ray is perpendicular to the boundary, no bending will occur:

Snell’s Law

The amount by which the wave is bent is given by Snell’s Law (ni and nr are the refractive indices of the media).

n ni i r rsin sin

Snell’s Law

Note that a ray will always bend towards the normal when travelling into a more-dense medium

Snell’s Law

Note that a ray will always bend towards the normal when travelling into a more-dense medium (and away from the normal when travelling into a less-dense medium).

Problem Solving with Snell’s Law

When light passes from air into water at an angle of 45o from the normal, what is the angle of refraction in the water?

Problem Solving with Snell’s Law

When light passes from air into water at an angle of 45o from the normal, what is the angle of refraction in the water?

?:

45

33.1

0.1:

water

air

water

air

U

n

nG

Problem Solving with Snell’s Law

When light passes from air into water at an angle of 45o from the normal, what is the angle of refraction in the water?

?:

45

33.1

0.1:

water

air

water

air

U

n

nG

Problem Solving with Snell’s Law

When light passes from air into water at an angle of 45o from the normal, what is the angle of refraction in the water?

?:

45

33.1

0.1:

water

air

water

air

U

n

nG

water

airairwater

waterwaterairair

n

n

nnS

sin

sin

sinsin:

Problem Solving with Snell’s Law

When light passes from air into water at an angle of 45o from the normal, what is the angle of refraction in the water?

?:

45

33.1

0.1:

water

air

water

air

U

n

nG

water

airairwater

waterwaterairair

n

n

nnS

sin

sin

sinsin:

Problem Solving with Snell’s Law

When light passes from air into water at an angle of 45o from the normal, what is the angle of refraction in the water?

?:

45

33.1

0.1:

water

air

water

air

U

n

nG

water

airairwater

waterwaterairair

n

n

nnS

sin

sin

sinsin:

32)53166.0(sin

53166.033.1

45sin)0.1(sin:

1water

waterS

Dispersion

Note that since different wavelengths of white light refract slightly differently, refraction can split white light into its different wavelengths (i.e. colours) especially if refracted twice.

Dispersion

Note that since different wavelengths of white light refract slightly differently, refraction can split white light into its different wavelengths (i.e. colours) especially if refracted twice.

Dispersion

Note that since different wavelengths of white light refract slightly differently, refraction can split white light into its different wavelengths (i.e. colours) especially if refracted twice.

This is called dispersion.