1

Light

Chapters 36 – 39

2

Wave or Particle?

Newton -- particles.In the early 19th century, Young, Fresnel,

and others -- wave.In 1860 Maxwell -- electromagnetic wave.

3

Photoelectric effect

19th century -- Hertz -- shining light on a metal plate would make it emit electrons – producing an electric current.

Kinetic energy of the emitted electrons was independent of the intensity of the light.

Not wave theory

4

Photons

In 1905 Einstein proposed that light is quantized in small bundles called photons.

The energy of a photon depends on the frequency of the light, not the intensity.

5

Wave Particle Duality

In some situations, light behaves like a wave.

In other situations, it behaves like a particle.

This unit will only deal with light as a wave.

6

Light Basics

Light is an electromagnetic wave.

Doesn’t need a medium to travel

Travels at the speed of light

7

Speed of light

8

Speed of Light

Defined as 299 792 458 m/s

We use 3.00 x 108 m/s

Denoted as the letter c

9

Electromagnetic Spectrum

We detect a very small part of the electromagnetic spectrum as visible light.

10

Visible Spectrum

We can see wavelengths from about 400 to 700 nm.

Different wavelengths correspond to different colors.

11

Wave Front

Leading edge of a wave Shows the crests of the wave

12

Ray Model

A ray is an imaginary line along the direction of travel of a wave.

13

Reflection

14

Law of Reflection

The angle of reflection equals the angle of incidence.

Angles are measured from the normal, not the surface.

15

Example A ray reflects off 2 perpendicular mirrors. How does its final direction relate to its initial direction?

30°

30°

60°

60°

60°

60°

30°

anti-parallel

16

You tryRepeat example for 2 mirrors at a 60° angle.

90°

60°

30° 60°60°

anti-parallel

17

Speed of Light in MatterThe speed of light in a transparent material

such as air, water, or glass is less than the speed of light in a vacuum.

Each material has an index of refraction, n, where

Can n be greater than 1?Less than 1?Equal to 1?

v

cn

18

Refraction When light travels from one material into another,

its path is bent. If the second material has a higher index of

refraction, it is bent towards the normal.

19

Color

The index of refraction of a material has a slight dependence on wavelength.

Red (longer wavelength) is refracted less than violet (shorter wavelength).

20

Prisms

21

Rainbows

Rainbows are reflected light from water droplets in the air.

Different colors are refracted at different angles by the water, so they are separated.

22

Snell’s Law2211 sinsin nn

2sin33.145sin 322

23

You try

Light traveling in glass with n = 1.5 enters air with an angle of incidence of 30°.

What is the angle of refraction?

2211 sinsin nn

2sin130sin5.1 492

Did the light bend toward the normal or away from it?

24

Wavelength in new material

For any wave, the wavelength l and the frequency f are related by the equation

During refraction, the frequency does not change.

fv

25

Wavelength in new material

0fc fv

fn

c

fc

0 f

n

c

26

Wavelength in new material

n

cc

0

n0

27

Mirages

28

Mirages

29

Total Internal Reflection

30

Total Internal Reflection90sinsin 21 nn c

What if n2 is greater than n1?

1

2sinn

nc

31

Total Internal Reflection

33.11 waternn

00.12 airnn

1

2sinn

nc 33.1

00.1sin c

49c

32

Fiber Optics

33

q

q

Plane Mirrors

Image is same distance from mirror. Image is the same size. Image is upright.

mirror

objectimage

34

Real Images

An image is real if the light rays actually converge at that location.

A real image can be shown on a card or screen.

A real image is located in front of the mirror.

35

Virtual Images

An image is virtual if the light rays only appear to converge at that location.

A virtual image cannot be shown on a card or screen.

A virtual image is located behind the mirror.

36

Depth Inversion

The front and back of an object are reversed in a plane mirror.

This causes right and left to be reversed between the object and the image.

37

Spherical Mirrors

In spherical mirrors, the mirror is on the inner or outer surface of part of a hollow sphere.

38

Concave Mirrors

Reflect light from inner surface of sphere. Are “caved in”. Also called converging.

39

Mirrors

C is the center of the sphere. r is the radius of curvature. F is the focal point. f is the focal length.

Principal axisC F

r

f

2

rf

40

Finding the image 1

Image is inverted. Image is real.

Principal axisF

41

Concave Mirrors

To find the image Draw a ray parallel to the principal axis.

– It will reflect through the focal point. Draw a ray through the focal point.

– It will reflect parallel to the principal axis. The image is located at the intersection of the two

reflected rays. You can draw a ray to the center of the mirror. It

will reflect according to the law of reflection for flat surfaces.

42

Convex Mirrors

Reflect light from outer surface of sphere. Also called diverging.

43

Finding the image 2

Image is upright. Image is virtual.

FF

44

Convex MirrorsTo find the imageDraw a ray parallel to the principal axis.

– It will reflect as if it had come from the focal point.

Draw a ray through the focal point.– It will reflect parallel to the principal axis.– Extend the parallel reflected ray behind the

mirror.The image is located at the intersection of

the two reflected rays (or their extensions).

45

Mirror Practice 1

Image is upright or inverted.Image is real or virtual.

F

46

Mirror Practice 2

Image is upright or inverted.Image is real or virtual.

F

No Image!

47

Mirror Practice 3

Image is upright or inverted.Image is real or virtual.

FF

48

Mirror Practice 4

Image is upright or inverted.Image is real or virtual.

FF

49

The Mirror Equation

Used to locate the image mathematically. do = object distance

di = image distance f = focal length r = radius of curvature

fdd io

111

rdd io

211

50

Mirror Conventions

do is always positive.

di is positive for real images. – Same side of mirror as object.

di is negative for virtual images. – Opposite side of mirror as the object.

51

Mirror Conventions

f is positive for a converging (concave) mirror.

f is negative for a diverging (convex) mirror.

52

Magnification

Ratio of the image size to the object size.

Same as the negative of the ratio of the image distance to the object distance.

m hi

ho

d i

do

53

Magnification

Negative magnification means the image is inverted.

Magnification between 1 and –1 means the image is smaller than the object.

54

Example

Scenario from mirror practice 4.

cm 10od cm 10f

fdd io

111

do is always positive.f is negative for a diverging (convex)

mirror.

cm 30 h

55

Example

Negative sign means virtual image

10

11

10

1

id

5

11

id5id

56

Example

Find the magnification of the image

m hi

ho

d i

do 10

5m

5.0m

Positive means upright image.Image is half as big as object.

5.1ih

57

Thin Lenses

Lenses are considered thin if their thickness is considerably smaller than their focal length.

Can be concave or convex, like mirrors.

Form images by refraction.

58

Convex Lenses

Convex lenses are converging.– Opposite of mirrors.

59

Finding the image 3

Image is inverted.Image is real.

F F

60

Convex lenses

To Find the image Draw a ray parallel to the axis.

– It will refract through the far focal point. Draw a ray through the near focal point.

– It will refract parallel to the axis. You can also draw a ray through the center of the

lens. It will continue straight through the lens without being bent.

The image is located at the intersection of the two refracted rays.

61

Concave Lenses

Concave lenses are diverging.– Opposite of mirrors.

62

Finding the image 4

Image is upright.Image is virtual.

F

63

Concave Lenses

To find the image Draw a ray parallel to the principal axis.

– It will be refracted as if it came from the focal point.– Extend this ray behind the lens.

Draw a ray through the center of the lens.– It will go straight through the lens.

The image forms at the intersection of the refracted rays (or their extensions).

64

Lens practice 1

F F

Image is upright or inverted.Image is real or virtual.

65

Lens practice 2

F F

Image is upright or inverted.Image is real or virtual.

No Image!

66

Lens practice 3

Image is upright or inverted.Image is real or virtual.

F

67

Lens practice 4

Image is upright or inverted.Image is real or virtual.

F

68

The Lens Equation

The same as the mirror equation.

Magnification is also the same as for mirrors.

69

Lens Conventions

do is always positive.

di is positive for real images. – Opposite side of lens as the object.

di is negative for virtual images. – Same side of lens as object.

f is positive for a converging lens.f is negative for a diverging lens.

70

The eye

Diagram on page 872Light is refracted at the cornea and the lens.A real image is formed on the retina at the

back of the eye.The optic nerve sends the data to the brain.Vision is best in a small central region.

71

The eye

For a clear vision, the image must be formed exactly at the retina.

This distance, di does not change.

In order to focus objects at varying do distances, the focal length of the lens must change.

The eye does this by bending the lens.

72

Near point

The shortest object distance you can see clearly.

Depends on the ability of your muscles to bend your lens.

Muscle flexibility decreases with age, so the near point increases.– Reading glasses needed

73

Myopic eyes

Near-sighted.The eye is too long, so the image forms in

front of the retina.Too much convergence – needs a diverging

lens to correct.

74

Hyperopic eye

Far-sightedThe eye is too short, so the image forms

behind the retina.Not enough convergence – needs a

converging lens to correct.

75

astigmatism

The cornea is not spherical.Cannot focus on horizontal and vertical

lines at the same time.Corrected with a cylindrical lens – curved

in one direction.

76

diopters

The power of a lens is measured in diopters.The power is the reciprocal of the focal

length in meters.How glasses are prescribed.The numbers on your contacts.

77

LASIK

Laser reshapes cornea to refract light differently.

Cornea must be sufficiently thick.Works best for near-sightedness and

astigmatism.Will not increase lens flexibility

– Reading glasses may still be needed.

78

cameras

The film is like the retina in your eye.The area of the lens is adjusted by the

aperture.Aperture size is described by the “f-

number”, which is the focal length divided by the diameter.

79

Interference

Principle of linear superposition:– When two or more waves overlap, the resultant

displacement at any point and at any instant may be found by adding the instantaneous displacements that would be produced at the point by the individual waves

– You just add them

80

81

Two source interference

Thomas Young

82

Two Source InterferenceFrom the diagram we can see that

L

ymm tan

If we use the fact that for very small angles, tan q is about sin q, we can say

L

ymm sin

83

Approximation

If we assume that the distance L from the slits to the screen is much larger than the spacing, d, between the slits, then we can say that the path length between the two rays r1 and r2 is

sin21 drr

84

Two Source interference

md m sin

In order to have constructive interference from the light from two adjacent slits, the path difference between their light rays must be a complete wavelength.

d

mLym

85

Diffraction GratingsConsist of a large number of equally spaced

lines or slits on a flat surface.N is the number of slits per unit length

(such as mm or cm)d is the distance between two adjacent slits.

Nd

1

86

Diffraction gratings

Use the same equations as two source interference.

However, the patterns produced are sharper and narrower