CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

College Physics B - PHY2054C

Wave Optics

10/27/2014

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CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Outline

1 Thin-Lens Equation

2 Geometrical Optics

Rainbows

Aberrations

3 Wave Optics

Interference

Michelson Interferometer

Thin-Film Interference

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Lens Equation & Magnification

The thin-lens equation is found from

analysis of the similar triangles:

1

so+

1

si=

1

f

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Lens Equation & Magnification

The thin-lens equation is found from

analysis of the similar triangles:

1

so+

1

si=

1

f

The magnification can be found

from the similar triangles shown:

m =hi

ho= −

si

so

These results are identical to the

results found for mirrors.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Review Question 1

A fish swims below the surface of the water at P. An observer

at O sees the fish at

A a greater depth than it really is.

B the same depth.

C a smaller depth

than it really is.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Review Question 1

A fish swims below the surface of the water at P. An observer

at O sees the fish at

A a greater depth than it really is.

B the same depth.

C a smaller depth than it really is.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Review Question 2

A fish swims below the surface of the water. Let’s suppose an

observer is looking at the fish from point O ′ – straight above

the fish. The observer sees the fish at

A a greater depth than it really is.

B the same depth.

C a smaller depth

than it really is.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Review Question 2

A fish swims below the surface of the water. Let’s suppose an

observer is looking at the fish from point O ′ – straight above

the fish. The observer sees the fish at

A a greater depth than it really is.

B the same depth.

C a smaller depth

than it really is.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Review Question 3

A parallel beam of light is sent through an aquarium. If a convex

glass lens is held in the water, it focuses the beam

A closer to the lens than

B at the same position as

C farther from the lens than

outside the water.

Indices of Refraction

Air 1.0003

Glass ∼ 1.47

Water 1.33

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Review Question 3

A parallel beam of light is sent through an aquarium. If a convex

glass lens is held in the water, it focuses the beam

A closer to the lens than

B at the same position as

C farther from the lens than

outside the water.

Indices of Refraction

Air 1.0003

Glass ∼ 1.47

Water 1.33

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Outline

1 Thin-Lens Equation

2 Geometrical Optics

Rainbows

Aberrations

3 Wave Optics

Interference

Michelson Interferometer

Thin-Film Interference

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Rainbows

Incident ray from Sun is refracted when it enters water droplet:

• The refracted angle depends on the color of the light.

• Rays for different colors travel at different angles.

• When light reaches the back surface, a portion is reflected.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Rainbows

Incident ray from Sun is refracted when it enters water droplet:

• Reflected rays refracted again when they leave droplet.

• The outgoing rays emerge over a range of angles.

➜ Different colors of a rainbow appear at different positions

(angles) in the sky.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Rainbows

Incident ray from Sun is refracted when it enters water droplet:

• Reflected rays refracted again when they leave droplet.

• The outgoing rays emerge over a range of angles.

➜ Different colors of a rainbow appear at different positions

(angles) in the sky.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Chromatic Aberration

Different colors are actually diffracted by different amounts:

• The focal length of a lens is different for each color.

• Multiple lenses can be used to minimize the effect.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Outline

1 Thin-Lens Equation

2 Geometrical Optics

Rainbows

Aberrations

3 Wave Optics

Interference

Michelson Interferometer

Thin-Film Interference

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Wave Optics

The field of wave optics studies properties of light that depend

on its wave nature:

• Originally light was thought to be a particle and that model

successfully explained the phenomena discussed in

geometric options.

• Other experiments revealed properties of light that could

only be explained with a wave theory.

• Maxwell’s theory of electromagnetism convinced physicists

that light was a wave.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Wave Optics

The wavelength of light plays a key role in determining when

geometric optics can or cannot be used:

1 When discussing image characteristics over distances

much greater than the wavelength, geometric optics is

extremely accurate.

2 When dealing with sizes comparable to or smaller thanthe wavelength, wave optics is required.

• Examples include interference effects and propagation

through small openings.

➜ Even more experiments led to the quantum theory of light.

Light has properties of both waves and particles.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Interference

One property unique to waves is interference:

A When two sound waves are in phase, their maxima occur

at the same time at a given point in space.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Interference

The total wave displacement at the listener’s location is the sum

of the displacements of the two individual waves:

B If two waves are in phase, the sum of their displacements

is large. The waves interfere constructively.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Interference

The maximum of one wave can coincide with the minimum of

the other wave. These waves are out of phase.

C The interference is destructive when the waves are out of

phase.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Question 4

That light can undergo interference is evidence that it:

A has electric properties.

B is made of corpuscles.

C behaves like a wave.

D has a phase of 180◦.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Question 4

That light can undergo interference is evidence that it:

A has electric properties.

B is made of corpuscles.

C behaves like a wave.

D has a phase of 180◦.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Conditions for Interference

Two waves can interfere if all the following conditions are met:

1 Two or more interfering waves travel through different

regions of space over at least part of their propagation

from source to destination.

2 The waves are brought together at a common point.

3 The waves must have the same frequency and must alsohave a fixed phase relationship:

• This means that over a given distance or time interval the

phase difference between the waves remains constant.

➜ Such waves are called coherent.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Question 5

Waves from a radio station have a wavelength of 250 m. These

waves can travel directly from the antenna to a receiver or can

reflect from a nearby mountain cliff and then reach the receiver.

If the distance from the receiver to the cliff is L = 1000 m, is

there

A constructive

B destructive

C no

interference at the receiver?

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Question 5

Waves from a radio station have a wavelength of 250 m. These

waves can travel directly from the antenna to a receiver or can

reflect from a nearby mountain cliff and then reach the receiver.

If the distance from the receiver to the cliff is L = 1000 m, is

there

A constructive

B destructive

C no

interference at the receiver?

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Michelson Interferometer

The Michelson interferometer is based on the interference of

reflected waves:

• Two reflecting mirrors

are mounted at right

angles.

• A third mirror is partially

reflecting (beam splitter).

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Michelson Interferometer

The Michelson interferometer is based on the interference of

reflected waves:

• The incident light hits the

beam splitter and is then

divided into two waves.

• The waves reflect from the

mirrors at the top and right

and then recombine at the

beam splitter.

• Only difference between

the two waves is that they

travel different distances

between their respective

mirrors and the beam

splitter.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Michelson Interferometer

The Michelson interferometer is based on the interference of

reflected waves:

The path length difference is:

∆L = 2L 2 − 2L 1

The path length difference is

related to wavelength of the

light:

N =∆L

λ

• N integer/half-integer:

constructive/destructive

interference

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Interference

The Michelson interferometer is based on the interference of

reflected waves:

The path length difference is:

∆L = 2L 2 − 2L 1

The path length difference is

related to wavelength of the

light:

N =∆L

λ

• N integer/half-integer:

constructive/destructive

interference

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Interference

The Michelson interferometer is based on the interference of

reflected waves:

The path length difference is:

∆L = 2L 2 − 2L 1

Interference Conditions

• Constructive interference:

(large intensity)

∆L = m λ

• Destructive interference:

(zero intensity)

∆L = (m + 1/2)λ

➜ Measurement of length.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Thin-Film Interference

Assume a thin soap film rests on a flat glass surface.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Thin-Film Interference

Assume a thin soap film rests on a flat glass surface.

The upper surface of the soap film is similar to the beam splitter

in the interferometer:

• It reflects part of the incoming light and allows the rest to

be transmitted into the soap layer after refraction at the

air-soap interface.

• The transmitted ray is

partially reflected at the

bottom surface.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Thin-Film Interference

Assume a thin soap film rests on a flat glass surface.

The upper surface of the soap film is similar to the beam splitter

in the interferometer:

• It reflects part of the incoming light and allows the rest to

be transmitted into the soap layer after refraction at the

air-soap interface.

• The transmitted ray is

partially reflected at the

bottom surface.

• The two outgoing rays meet

the conditions for interference:

1 Travel through different regions

2 Recombination

3 Coherence

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Thin-Film Interference

Assume a thin soap film rests on a flat glass surface.

Index of refraction of the film also needs to be accounted for:

• From the speed of the wave inside the film:

λ film f film =c

n film

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Thin-Film Interference

Assume a thin soap film rests on a flat glass surface.

Index of refraction of the film also needs to be accounted for:

• From the speed of the wave inside the film:

λ film f film =c

n film

• The wavelength changes as the

light wave travels from a vacuum

into the film:

λ film =v

f=

c/n film

f

=λ vac

n film

≈

λ air

n film

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Thin-Film Interference

Assume a thin soap film rests on a flat glass surface.

Index of refraction of the film also needs to be accounted for:

• The wavelength changes as the

light wave travels from a vacuum

into the film:

λ film =v

f=

c/n film

f

=λ vac

n film

≈

λ air

n film

• Number of extra wavelengths:

N =2d

λ film

=2d

λ/n film

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Frequency of Wave at Interface

When a light wave passes from one medium to another, the

waves must stay in phase at the interface. The frequency must

be the same on both sides of the interface.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Frequency of Wave at Interface

1 There is a phase change whenever the index of refraction

on the incident side is less than the index of refraction of

the opposite side (wave is inverted).

2 If the index of refraction is larger on the incident side the

reflected ray in not inverted and there is no phase change.

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Phase Changes in a Thin Film

The total phase change in a thin film must be accounted for:

• The phase difference due to the extra distance traveled

by the ray.

• Any phase change due to reflection.

• For a soap film on glass: n air < n film < n glass

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Phase Changes in a Thin Film

There are phase changes for both reflections at the soap film

interfaces:

B The reflections at both the top and bottom surfacesundergo a 180◦ phase change:

1 If the number of extra cycles, N, is an integer, there is

constructive interference: 2d = mλ/n film

2 If the number of extra cycles is a half-integer, there is

destructive interference: 2d = (m + 1/2)λ/n film

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Phase Changes in a Thin Film

Assume the soap bubble is surrounded by air.

C There is a phase change at the top of the bubble. Thereis no phase change at the bottom of the bubble:

1 If the number of extra cycles, N, is a half-integer, there is

constructive interference: 2d = (m + 1/2)λ/n film

2 If the number of extra cycles is an integer, there is

destructive interference: 2d = mλ/n film

CollegePhysics B

Thin-LensEquation

GeometricalOptics

Rainbows

Aberrations

Wave Optics

Interference

Michelson

Interferometer

Thin-Film

Interference

Phase Changes in a Thin Film

Assume the soap bubble is surrounded by air.

C There is a phase change at the top of the bubble. Thereis no phase change at the bottom of the bubble:

1 If the number of extra cycles, N, is a half-integer, there is

constructive interference: 2d = (m + 1/2)λ/n film

2 If the number of extra cycles is an integer, there is

destructive interference: 2d = mλ/n film