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Homework #1

Reading: Chaps. 14, 20, 21, 23

Suggested exercises: 23.6, 23.7, 23.8, 23.10,

23.12, 23.13, 23.14, 23.15

Problems: 23.39, 23.40, 23.41, 23.42, 23.44 ,23.45, 23.47, 23.48, 23.49, 23.53, 23.54 (due:

Fri., Aug. 28)

A Brief History of Light

Willebrod Snell 1580-1626 Dutch

discovered law of refraction (Snell's law)

A Dutch mathematician who is best known for the

law of refraction, a basis of modern geometric

optics; but this only become known after his death

when Huygens published it.

Sir Isaac Newton 1643-1727 English

developed theories of gravitation and mechanics, and

invented differential calculus

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A Brief History of Light

Robert Hooke 1635-1703 English

discovered Hooke's law of elasticity

made contributions to many different fields including

mathematics, optics, mechanics, architecture and

astronomy. He had a famous quarrel with Newton.

Christiaan Huygens 1629-1695 Dutch

proposed a simple geometrical wave theory of light,

now known as ``Huygen's principle''; pioneered use of

the pendulum in clocks

A Brief History of Light

Thomas Young 1773-1829 British

studied light and color; known for his double-slit

experiment that demonstrated the wave nature of light

did work in surface tension, elasticity, and gave one of

the earliest scientific definitions of energy. His studies

of the Rosetta stone contributed greatly to the

deciphering of the ancient Egyptian hieroglyphic

writing.

Augustin-Jean Fresnel 1788-1827 French

studied transverse nature of light waves, and he was

one of the founders of the wave theory of light.

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A Brief History of Light

James Clerk Maxwell 1831-1879 Scottish

propounded the theory of electromagnetism;

developed the kinetic theory of gases

Chapter 23. Ray Optics (Geometric Optics)

Our everyday experience

that light travels in straight

lines is the basis of the ray

model of light. Ray optics

apply to a variety of

situations, including mirrors,

lenses, and shiny spoons.

Chapter Goal: To

understand and apply the ray

model of light.

Lecture #1

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Topics:

• The Ray Model of Light

• Principles governing Ray model:

Reflection

Refraction

• Image Formation by Refraction

• Color and Dispersion

• Thin Lenses: Ray Tracing

• Thin Lenses: Refraction Theory

• Image Formation with Spherical Mirrors

Chapter 23. Ray Optics

Chapter 23. Basic Content and Examples

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Propagation

In a homogenous medium, a light ray propagates

along a straight line

Point light

source

Object

Shadow

Propagation

http://www.youtube.com/watch?v=WVuV_xVDJDY

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Ray Model of Light

• Light rays travel in straight lines

• Light ray can cross

• A light ray travels forever unless it interacts

with matter (why?)

• An object is a source of light rays (self-

luminous objects or reflective objects)

• The eye sees by focusing a diverging bundle of

rays

Definitions

• Object

• Point source

• Parallel bundle (beam)

• Aperture

Questions regarding shadows: point source, parallel

source, no shadow?

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Reflection

Specular reflection Diffuse reflection

Light interacts with an opaque object.

Reflection

The law of reflection states that

1. The incident ray and the reflected ray are in the same

plane normal to the surface (incident plane)

2. The angle of reflection equals the angle of incidence:

θr = θi

How about

reflection from a

curved surface?

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The Plane Mirror

s s’

The Plane Mirror

Consider P, a source of rays which reflect from a mirror. The reflected rays appear to emanate from P', the same distance behind the mirror as P is in front of the mirror. That is, s' = s.

Virtual image

Under what condition can

you see the image of the

object?

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Refraction

Light interacts with transparent object.

Refraction

Light interacts with transparent object.

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Refraction

Snell’s law states that if a ray refracts between medium 1 and medium 2, having indices of refraction n1 an n2, the ray angles θ1 and θ2 in the two media are related by (1621

Willebrord Snellius, Dutch mathematician)

Notice that Snell’s law does not mention which is the incident angle and which is the refracted angle.

v

c

mediumainlightofSpeed

vacuuminlightofSpeedn

Index of refraction

Speed of Light

In vacuum,

smc /109979.2 8

In medium,

cv

Thus,n 1

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Can n be negative?

What would happen if

n becomes negative?

http://en.wikipedia.org/wiki/Metamaterial

http://people.ee.duke.edu/~drsmith/negativ

e_index_about.htm

Metamaterials !!!

Electromagnetic cloaking devices, super lenses, filters,

sub wavelength waveguides and antennas

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Refraction

2211 sinsin nn

If n1 < n2, then θ1 > θ2

Snell’s law

n1

n2

1

2

Refraction

2211 sinsin nn Snell’s law

n1

n2

1

2

If n1 > n2, then θ1 < θ2

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Refraction

2211 sinsin nn Snell’s law

n1

n2

If θ1 = 0, then θ2 = 0, regardless the values of n1 and n2

Total Internal Reflection

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Total Internal Reflection

2211 sinsin nn

If n2 < n1, then θ2 > θ1

cn

n sinsin

1

21 When

o902 1

21sin

n

nWhen

Total internal reflection occurs

n1

n2

Snell’s law

1

2

12 sinsin

n

n

Total Internal Reflection

Optical fibersA laser bouncing down a perspex rod

illustrating the total internal reflection of light

in a multimode optical fiber

Charles Kuen Kao

The Nobel Prize in Physics 2009Watch this video:

https://www.youtube.com/watch?v=0MwMkBET_5I

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Total Internal Reflection

Invisible Glass

https://www.youtube.com/watch?v=wlELYZJ5JF4

Why does the glass rod vanish in another liquid?

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Color

Different colors are associated with light of different wavelengths. The longest wavelengths are perceived as red light and the shortest as violet light.

Color Questions

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Dispersion

The slight variation of index of refraction with wavelength is known as dispersion.

Notice that n is larger when the wavelength is shorter, thus violet light refracts more than red light.

Dispersion

https://www.youtube.com/watch?v=uucYGK_Ymp0

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Dispersion

https://www.youtube.com/watch?v=uucYGK_Ymp0

Dispersion

If n1 < n2,

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Dispersion

If n1 > n2,

Rainbow

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Three Laws of Geometric Optics

1. Propagation in homogenous medium

2. Law of reflection

3. Law of refraction

Ray Model

Example 1.1

An albatross glides at a constant 15m/s horizontally above level

ground, moving in a vertical plane that contains the Sun. It glides

toward a solid wall of height h = 2.0 m, which it will just barely

clear. At that time of day, the angle of the Sun relative to the

ground is = 30o. At what speed does the shadow of the albatross

move (a) across the level ground and the (b) up the wall?

h

Sunray

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Reflection

The following figure shows light reflecting from two

perpendicular reflecting surfaces A and B. Find the

angle between the incoming ray i and the outgoing ray

r’.

i

r r’A

B

In-Class Activity #1

Reflection

In-Class Activity #2

The following figure shows the

multiple reflections of a light ray

along a glass corridor where the

walls are either parallel or

perpendicular to one another. If the

angle of incident at point a is 30o,

what are the angles of reflection of

the light at point b, c, d, e, and f?

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Example 1.2

A basketball player with a height of 191cm wants to see

his entire height in a “full-length” mirror mounted on a

wall. What is the least length the mirror must have?

Example 1.3

In the figure you look into a system of two vertical parallel mirrors A

and B separated by distance d. A toy monkey is hanged at point O, a

distance 0.2d from mirror A. Each mirror produces a first (least deep)

image of the monkey. Then each mirror produces a second image

with the object being the first image in the opposite mirror. Then each

mirror produces a third image with the object being the second image

in the opposite mirror, and so on – you might see hundreds of

monkey images. How deep behind mirror A are the first, second and

third images in mirror A?

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In-Class Activity #3

The following figure shows rays of monochromic light passing

through three materials a, b, and c. Rank the materials according to

their indexes of refraction, greatest first.

Tactics: Analyzing refraction

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EXAMPLE 23.4 Measuring the index of refraction

QUESTION:

EXAMPLE 23.4 Measuring the index of refraction

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EXAMPLE 23.4 Measuring the index of refraction

EXAMPLE 23.4 Measuring the index of refraction

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EXAMPLE 23.4 Measuring the index of refraction

EXAMPLE 23.4 Measuring the index of refraction

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Example 1.4

In the figure, a 2.00-m-long vertical pole extends from the

bottom of a swimming pool to a point 50.0 cm above the

water. Sunlight is incident at 55.0o above the horizon. What

is the length of the shadow of the pole on the level bottom

of the pool?

Example 1.5

The following figure shows a triangular prism of glass in

air; an incident ray enters the glass perpendicular to one

face and is totally reflected at the far glass – air interface

as indicated. If 1 is 45o, what can you say about the

index of refraction n of the glass?

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Example 1.6

A submerged swimmer is looking directly upward through

the air-water interface in a pool. Over what range of

angles do rays reach the swimmer’s eyes from light

sources external to the water? Assume that the light is

monochromatic and that the index of refraction of water is

1.33.

Similar to example 23.5

Optional Course Materials

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Reversibility of Rays

When the propagation direction of a light ray is

reversed, it will follow the same (old) path.

θi θr

n

θ2

1

2