Chapter 35 - Refraction

Objectives: After completing this module, you should be able to:

• Define and apply the concept of the index of refraction and discuss its effect on the velocity and wavelength of light.

• Determine the changes in velocity and/or wavelength of light after refraction.

• Apply Snell’s law to the solution of problems involving the refraction of light.

• Define and apply the concepts of total internal reflection and the critical angle of incidence.

Refraction

Water

Air Refraction is the bending of light as it passes from one medium into another.

refraction

N

qw

qA

Note: the angle of incidence qA in air and the angle of refraction qA in water are each measured with the normal N.

The incident and refracted rays lie in the same plane and are reversible.

Refraction Distorts Vision

Water

Air

Water

Air

The eye, believing that light travels in straight lines, sees objects closer to the surface due to refraction. Such distortions are common.

The Index of Refraction

The index of refraction for a material is the ratio of the velocity of light in a vacuum (3 x 108 m/s) to the velocity through the material.

c

v c

nv

Index of refraction

cn

v

Examples: Air n= 1; glass n = 1.5; Water n = 1.33

Example 1. Light travels from air (n = 1) into glass, where its velocity reduces to only 2 x 108 m/s. What is the index of refraction for glass?

8

8

3 x 10 m/s

2 x 10 m/s

cn

v

vair = c

vG = 2 x 108 m/s

Glass

Air

For glass: n = 1.50

If the medium were water: nW = 1.33. Then you should show that the velocity in water would be reduced from c to 2.26 x 108 m/s.

Analogy for Refraction

Sand

Pavement Air

Glass

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

3 x 108 m/s

3 x 108 m/s

2 x 108 m/s

vs < vp

A Simplified Form of the Law

1 1 2

2 2 1

sin

sin

v n

v n

q

q

Since the indices of refraction for many common substances are usually available, Snell’s law is often written in the following manner:

1 1 2 2sin sinn nq q

The product of the index of refraction and the sine of the angle is the same in the refracted medium as for the incident medium.

Example 3. Light travels through a block of glass, then remerges into air. Find angle of emergence for given information.

Glass

Air

Air

n=1.5

First find qG inside glass:

sin sinA A G Gn nq q

500

qG

q 0sin (1.0)sin50

sin1.50

A AG

G

n

n

qq

qG = 30.70

qG

sin sin sinA G G AA An n nqq q

Apply to each interface: qe = 500

Same as entrance angle!

The Many Forms of Snell’s Law:

Refraction is affected by the index of refraction, the velocity, and the wavelength. In general:

1 2 1 1

2 1 2 2

sin

sin

n v

n v

q

q

All the ratios are equal. It is helpful to recognize that only the index n differs in the ratio order.

Snell’s Law:

Example 4: A helium neon laser emits a beam of wavelength 632 nm in air (nA = 1). What is the wavelength inside a slab of glass (nG = 1.5)?

nG = 1.5; A = 632 nm

; GA A AG

G A G

n n

n n

(1.0)(632 nm)

1.5421 nmG

Note that the light, if seen inside the glass, would be blue. Of course it still appears red because it returns to air before striking the eye.

Glass

Air

Air

n=1.5 q

qG

q qG

Dispersion by a Prism

Red Orange Yellow Green Blue Indigo Violet

Dispersion is the separation of white light into its various spectral components. The colors are refracted at different angles due to the different indexes of refraction.

Total Internal Reflection

Water

Air

light

The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900.

When light passes at an angle from a medium of higher index to one of lower index, the emerging ray bends away from the normal.

When the angle reaches a certain maximum, it will be reflected internally.

i = r

Critical angle

qc

900

Example 5. Find the critical angle of incidence from water to air.

For critical angle, qA = 900

nA = 1.0; nW = 1.33

sin sinW C A An nq q

0sin 90 (1)(1)sin

1.33

AC

w

n

nq

Critical angle: qc = 48.80 Water

Air

qc

900

Critical angle

In general, for media where n1 > n2 we find that:

1

2

sin C

n

nq

Summary

1 2 1 1

2 1 2 2

sin

sin

n v

n v

q

q Snell’s

Law:

Refraction is affected by the index of refraction, the velocity, and the wavelength. In general:

c = 3 x 108 m/s

v

Index of refraction

cn

vMedium

n

Summary (Cont.)

The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900.

In general, for media where n1 > n2 we find that:

1

2

sin C

n

nq

n1 > n2

qc

900

Critical angle

n1

n2