Transcript PHY2054_04-05-11

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• HW set 10 due this week; covers Ch 24.5-9 (skip 24.8) and 25.1-3
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QUESTIONS? PLEASE ASK!
From last time…
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Constructive and Destructive
Interference
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Young’s double slit experiment

Bright fringe: d sin θbright = m λ
y bright =

m = 0, ± 1, ± 2 …
Dark fringe: d sin θbright = (m+1/2) λ
y dark

lL
m
d
lL æ
1ö
çç m + ÷÷ m = 0, ± 1, ± 2 …
=
d è
2ø
Thin film interference
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Three different media
Constructive and destructive
interference equations depend on
indices of refraction for each media
Interference in Thin Films
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Interference is due to the
interaction of the waves reflected
from both surfaces of the film
Ray 1 - phase change of 180°
with respect to the incident ray
Ray 2 - no phase change with
respect to the incident wave
Ray 2 travels an additional
physical distance of 2t in the film

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The wavelength λ is reduced by n
in the film  the optical path
length is 2 n t
Constructive interference

2 n t = (m + ½ ) λ


m = 0, 1, 2 …
takes into account both the
difference in optical path length for
the two rays and the 180° phase
change
Destructive interference

2nt=mλ
m = 0, 1, 2 …
Anti-reflection coatings

Two phase shifts

Constructive interference

2nt=mλ



m = 0, 1, 2 …
takes into account both the
difference in optical path
length for the two rays and
both 180° phase changes
Destructive interference

2 n t = (m + ½ ) λ

m = 0, 1, 2 …
Handling thin films problems

Identify the thin film causing the interference

Determine the indices of refraction in the film and the media on either side of
it
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Determine the number of phase reversals: zero, one or two

Interference is constructive if the path difference is an integral multiple of λ
and destructive if the path difference is an odd half multiple of λ

NOTE: The conditions are reversed if one of the waves undergoes a phase change
on reflection
Equation
1 phase reversal
0 or 2 phase
reversals
2nt = (m + ½) l
constructive
destructive
destructive
constructive
2nt = m l
Diffraction

Huygen’s principle – light waves
spread out after they pass through
slits


Diffraction occurs when waves pass
through small openings, around
obstacles or by sharp edges

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A good example was Young’s double
slit experiment
A single slit placed between a distant
light source and a screen produces a
diffraction pattern
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 diffraction
broad, intense central band
a series of narrower, less intense
secondary bands  secondary maxima
In between the secondary maxima are
a series of dark bands  minima
Cannot be explained by geometric
optics!!
Single Slit Diffraction
DEMO
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Huygen’s principle - each
portion of the slit acts as a
source
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Light from one side of the slit
interferes with light from the
other side
The resultant intensity on the
screen depends on the direction
θ
Wave 1 travels farther than
wave 3 by a path length
difference d = (a/2) sin θ
If d = l/2, the two waves cancel
each other and destructive
interference results
a
l
sin  
2
2
Single Slit Diffraction, 2
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Divide slit into 1/4, 1/6,
…
In general, destructive
interference occurs for a
single slit of width for:
a
l
sin   m
2
2


m = 1, 2, 3, …
Note: doesn’t give any
information about the
variations in intensity
along the screen
Single Slit Diffraction, 3

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Broad central bright
fringe flanked by
much weaker bright
fringes alternating
with dark fringes
Points of
constructive
interference lie
approximately
halfway between the
dark fringes
Problem 24.36, p 819

A screen is placed 50
cm from a single slit
that is illuminated
with light of
wavelength 680 nm
wavelength. If the
distance between the
first and third
minima is 3.0 mm,
what is the width of
the slit?
Polarization of Light
Waves

Each electron in an atom produces a
wave with its own orientation of E
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Electrons in oscillating sinusoidal
motion
unpolarized
Unpolarized light - all directions of the
electric field vector are equally possible
and lie in a plane perpendicular to the
direction of propagation of the light
A wave is said to be linearly
polarized if the resultant electric field
vibrates in the same direction at all
times at a particular point
Polarization can be obtained from an
unpolarized beam by
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Selective absorption
Reflection
Scattering
In Lasers
E
polarized
Polarization by Selective Absorption
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The most common technique for polarizing light
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Your sunglasses!!
Uses a material that
i) transmits waves whose electric field vectors in the plane
are parallel to a certain direction and
ii) absorbs waves whose electric field vectors are
perpendicular to that direction
Selective Absorption

ET = Eo cos 

I µ E2
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 IT = Io cos2 θ
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Io is the intensity of the polarized wave incident
on the analyzer
This is known as Malus’ Law and applies to any
two polarizing materials whose transmission axes
are at an angle of θ to each other
Problem 24.58, p 821

Plane-polarized light is incident on a
single polarizing disk, with the
direction of E0 parallel to the
direction of the transmission axis.
Through what angle should the disk
be rotated so the intensity of the
light is reduced by a factor of (a) 2,
(b) 4, and (c) 6?
Polarization by Reflection
Polarization by Reflection II
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
The angle of incidence
for which the reflected
beam is completely
polarized is called the
polarizing angle, θp
Brewster’s Law relates
the polarizing angle to
the index of refraction
for the material
n=

sinq p
cos q p
= tanq p
θp may also be called
Brewster’s Angle
Brewster’s
Angle
Polarization by Scattering

When light is incident on a system of
particles, the electrons in the medium
can absorb and reradiate part of the
light
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This process is called scattering
An example of scattering is the
sunlight reaching an observer on the
earth becoming polarized
The horizontal part of the electric field
vector in the incident wave causes the
charges to vibrate horizontally
The vertical part of the vector
simultaneously causes them to vibrate
vertically
Horizontally and vertically polarized
waves are emitted
Why is the sky blue?
Optical Activity
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Certain materials display the
property of optical activity
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A substance is optically active if it
rotates the plane of polarization of
transmitted light
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Also called birefringence
Optical activity occurs in a material
because of an asymmetry in the
shape of its constituent materials
Answer to 23.36
Answer to 23.58