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

• Determine the changes in Determine the changes in velocityvelocity and/or and/or wavelengthwavelength of light after refraction. of light after refraction.

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

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

Water

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

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

refraction

N

w

A

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

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

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

Water

Air

Water

Air

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

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

The The index of refractionindex of refraction for a material is the for a material is the ratio of the velocity of light in a vacuum (3 ratio of the velocity of light in a vacuum (3 x 10x 1088 m/s) to the velocity through the m/s) to the velocity through the material.material.

The The index of refractionindex of refraction for a material is the for a material is the ratio of the velocity of light in a vacuum (3 ratio of the velocity of light in a vacuum (3 x 10x 1088 m/s) to the velocity through the m/s) to the velocity through the material.material.

c

vc

nv

Index of refractioncn

v

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

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

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 If the medium were waterwater: : nnW W = = 1.331.33. . Then you should show that the velocity Then you should show that the velocity in water would be reduced from in water would be reduced from c c to to 2.26 x 102.26 x 1088 m/s m/s..

Sand

PavementAir

Glass

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

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

3 x 108 m/s

3 x 108 m/s

2 x 108 m/s

vs < vp

Medium 1

Medium 2

Consider two Consider two light rays. light rays. Velocities are Velocities are vv11 in medium 1 and in medium 1 and vv22 in med. 2. in med. 2.

Segment Segment RR is is common common hypotenuse to two hypotenuse to two rgt. triangles. Verify rgt. triangles. Verify shown angles from shown angles from geometry.geometry.

v1

v1t

v2

v2t11

RR

1 21 2sin ; sinv t v t

R R

11 1

22 2

sin

sin

v tvR

v t vR

1

2

Medium 1

Medium 2

The ratio of the The ratio of the sinesine of the of the angle of incidence angle of incidence 11 to the to the sinesine of the angle of of the angle of refraction refraction 22 is equal to the is equal to the ratio of the incident ratio of the incident velocity velocity vv11 to the refracted to the refracted velocity velocity vv22 ..

The ratio of the The ratio of the sinesine of the of the angle of incidence angle of incidence 11 to the to the sinesine of the angle of of the angle of refraction refraction 22 is equal to the is equal to the ratio of the incident ratio of the incident velocity velocity vv11 to the refracted to the refracted velocity velocity vv22 ..

Snell’s Law:

1 1

2 2

sin

sin

v

v

v1

v2

The incident angle is:The incident angle is:

AA = 90 = 9000 – 30 – 3000 = 60 = 6000

sin

sinA A

W W

v

v

8 0

8

sin (2 x 10 m/s)sin 60sin

3 x 10 m/sW A

WA

v

v

W = 35.30W = 35.30

AirAir

H2

O

303000

W

AA

Another form of Snell’s law can be derived Another form of Snell’s law can be derived from the definition of the index of from the definition of the index of refraction:refraction:

from which c c

n vv n

1 1 21

2 2 12

;

cv v nn

cv v nn

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 for Snell’s law for velocities and velocities and

indices:indices:

Medium 11

2

Medium 2

1 1 2

2 2 1

sin

sin

v n

v n

1 1 2

2 2 1

sin

sin

v n

v n

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

1 1 2 2sin sinn n

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

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

Glass

AiAirr

AiAirr

n=1.5

First find First find GG inside inside glass:glass:sin sinA A G Gn n

505000

G

0sin (1.0)sin 50

sin1.50

A AG

G

n

n

G = 30.70G = 30.70

From geometry, From geometry, note angle note angle GG same same for next interface.for next interface.

G

sin sin sinA G G AA An n n Apply to each Apply to each

interface:interface:e = 500e = 500

Same as entrance Same as entrance angle!angle!

The energy of light is determined by the The energy of light is determined by the frequency of the EM waves, which remains frequency of the EM waves, which remains constant as light passes into and out of a constant as light passes into and out of a medium. (Recall medium. (Recall v = fv = f..))

GlassAir

n=1n=1.5A

GfA= fG

GA

; A A A G G Gv f v f

; ;A A A A

G G G G

v f v

v f v

1 1 1

2 2 2

sin

sin

v

v

1 1 1

2 2 2

sin

sin

v

v

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

In general: In general:

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

In general: In general:

1 2 1 1

2 1 2 2

sin

sin

n v

n v

1 2 1 1

2 1 2 2

sin

sin

n v

n v

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

ratio order.

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

ratio order.

Snell’s Law:

nnGG = 1.5; = 1.5; AA = 632 nm = 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 Note that the light, if seen insideinside the glass, the glass, would be would be blueblue. Of course it still appears red . Of course it still appears red because it returns to air before striking the because it returns to air before striking the eye.eye.

Glass

AiAirr

AiAirr

n=1.5G

G

Red OrangeYellowGreenBlueIndigoViolet

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

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

Water

Air

light

The The critical angle critical angle cc is is the limiting angle of the limiting angle of incidence in a denser incidence in a denser medium that results in medium that results in an angle of refraction an angle of refraction equal to 90equal to 9000..

The The critical angle critical angle cc is is the limiting angle of the limiting angle of incidence in a denser incidence in a denser medium that results in medium that results in an angle of refraction an angle of refraction equal to 90equal to 9000..

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

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

i = r

Critical angle

cc

909000

For critical angle, For critical angle, A A = = 909000nnAA = 1.0;= 1.0; n nWW = 1.33 = 1.33

sin sinW C A An n 0sin 90 (1)(1)

sin1.33

AC

w

n

n

Critical angle:

c = 48.80 Water

Air

cc

909000

Critical angle

In general, for media In general, for media where where nn11 > > nn22 we find we find

that:that:

1

2

sin C

n

n 1

2

sin C

n

n

1 2 1 1

2 1 2 2

sin

sin

n v

n v

1 2 1 1

2 1 2 2

sin

sin

n v

n v

Snell’s Law:

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

In general: In general:

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

In general: In general:

c = 3 x 108 m/s

v

Index of refractioncn

vMedium

n

The The critical angle critical angle cc is is the limiting angle of the limiting angle of incidence in a denser incidence in a denser medium that results in medium that results in an angle of refraction an angle of refraction equal to 90equal to 9000..

The The critical angle critical angle cc is is the limiting angle of the limiting angle of incidence in a denser incidence in a denser medium that results in medium that results in an angle of refraction an angle of refraction equal to 90equal to 9000..

In general, for media where n1 > n2 we find

that:

1

2

sin C

n

n

n1 > n2

cc

909000

Critical angle

n1

n2