Aberrations Interference Wave Optics Interferometer
Transcript of Aberrations Interference Wave Optics Interferometer
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