Refraction and Snells Law

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

Analogy for Refraction

Sand

PavementAir

Glass

Light bends into glass then returns along original path Light bends into glass then returns along original path much as a rolling axle would when encountering a strip of much as a rolling axle would when encountering a strip of mud.mud.

Light bends into glass then returns along original path Light bends into glass then returns along original path much as a rolling axle would when encountering a strip of much as a rolling axle would when encountering a strip of mud.mud.

3 x 108 m/s

3 x 108 m/s

2 x 108 m/s

vs < vp

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

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:

n

cv

v

cnS :

?:

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

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

1 1 2

2 2 1

sin

sin

v n

v n

1 1 2

2 2 1

sin

sin

v n

v n

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

Question-12

In traveling from air into water (n = 1.33), a ray of light makesan angle of incidence of 52o.

Calculate the angle of refraction.

ClickClick

Question-11

A ray of light enters water at an angle of incidence of 30o.The angle of refraction is found to be 22o.

Calculate the index of refraction for water.

ClickClick

Question-13

In traveling from water into air, a ray of light makes an angleof refraction of 59o.

Calculate the angle of incidence.

ClickClick

Question-14

A ray of light emerges from water into air with an angle ofincidence of 22o. What is the angle of refraction?

ClickClick

Question-16

A light ray passes through two liquids,one floating on top of the other, in abeaker. The angle of refraction in thewater is 25o (see diagram).

Determine the angle of incidence (Ao).

ClickClick

Links

http://www.rpi.edu/dept/phys/ScIT/InformationTransfer/reflrefr/rr_sample/rrsample_15.html

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.