Wave Optics

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Wave Optics
Particle or wave?

• Interference and other Mysteries Explained

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You Predict

• What happens when a pitcher throws lots of
  fastballs at two holes?
• What pattern do you see on the wall beyond?

3
Predict This

• What happens when a beam of light goes through
  two tiny slits?
• What pattern do you expect on the screen beyond?

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Double Slit Interference Applet

• What if light from two slits interferes?
• http//www.ece.gatech.edu/research/ccss/education/
  Java/1998.Winter/Projects/pierce-woods/project/bin
  /projApp.htm
• Experiment performed by Young in 1801
• Convincing evidence for wave nature of light
• Another Double Slit Applet

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Double Slit Derivation

• http//noether.physics.ubc.ca/Teaching/Physics101/
  StudySheets/Double.html

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Understanding Path Difference

• dsinq Dd is the path difference for waves
  traveling to a given point on the fringe pattern
• If path difference is an integer number of
  wavelength, interference is constructive
• (bright fringe)
• If path difference is a half integer number of
  wavelengths, interference is destructive
• (dark fringe)

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Line Spacing

• d sinq ml m 0, 1, 2 constructive
• d sinq (m 1/2) l m 0, 1, 2 destructive
• x Lq Lml/d for bright fringes
• using sinq q q in radians

x
q tanq x/L
q
d
L
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What Will Happen to the Fringe Spacing

• x Lml/d
• if the wavelength increases?
• if the distance to the screen increases?
• if the slit width increases?

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Find l

• x Lml/d
• l dx/Lm 6.12 x 10 7 m 612 nm
• x 2.5 mm
• L 2.6 m
• d 0.6 mm
• l 5.78 x 10 7 m 578 nm

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Varying the Slit Separation
Courtesy of Siltec Ltd. http//www.infoline.ru/g23
/5495/Physics/English/feedback.htm
11

• x Lml/d
• lxd/L for adjacent fringes 4x10-3 x 5x10-4
• 
  2.6
• 7.7 x 10-7 770 nm

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Problem

• When white light passes through two slits 0.50mm
  apart an interference pattern appears on a screen
  2.5m away. The fringe separation is 2.5 mm for
  the violet light. Find the wavelength of this
  light.

Hint solve x Lml/d for l
L dx/mL dx/L 5.0 x 10-7 m 500nm
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Single Slit Interference

• Also called diffraction
• Fringes are larger
• Size of fringes decreases out from center of
  pattern
• Derivation http//oldsci.eiu.edu/physics/DDavis/11
  60/Ch25WO/Diff.html

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Homework

• Ch 24 Problems
• 3,5,7,9,10(613 nm), 11

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More On Single Slit Interference

• Pattern dominated by central maximum
• Called central diffraction maximum
• Width measured from minimum to minimum
• Twice as wide as other fringes
• Much brighter than other fringes

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Single Slit Diffraction- Varying the Slit Width

• Fringes get bigger as slit gets smaller

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Double Slit vs. Single Slit

• Double
• d sinq ml bright
• d sinq (m 1/2) l
• Dark
• modest central maximum
• m0,1,2,etc

• Single
• d sinq ml dark
• d sinq (m 1/2) l
• bright
• Dominant central maximum
• Fringes usually larger
• m1,2,3, etc

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Single Slit Problem

• 500 nm light is incident on a slit of width 0.001
  mm which is 1.0 m from a screen. Find the width
  (2q ) of the central diffraction maximum. (hint
  use dsinq ml )
• 60 degrees

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Dispersion

• Spreading of white light into spectrum of
  wavelengths

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Why Dispersion Occurs

• Index of refraction, n, depends on wavelength l
• Typically n decreases as l increases
• Exit angle from prism depends on l

White light
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Forming a Rainbow

• Java Applet

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Diffraction Gratings

• Diffraction Grating has thousands of lines per cm
  cut into glass plate
• Light from each slit interferes with light from
  all other slits
• Analysis like Double Slit
• Sin q ml/d principal maxima (bright)
• Lines very close so maxima occur at large angles
• Q 900 is maximum possible so only a few maxima
  (orders)exist

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Courtesy http//fermi.bgsu.edu/stoner/P202/interf
ere/sld015.htm
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Grating Set-Up

1. Mercury lamp
2. Spectrometer
3. Gratings

Courtesy http//physics.okstate.edu/courses/experi
ments/o5.html
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How Grating Works in Practice

• Purpose is to analyze spectrum of light from
  source such as unknown gas or a star

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Spectrum Produced by Grating
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Diffraction Grating Problem

• A grating contains 5000 lines per cm
• Find the slit separation (d) in meters
• 500 nm light is incident on the grating.
• At what angles will the first, second and third
  orders be observed? Is there a fourth order?
• Hint use Sin q ml/d

2 x 10-6 m
0.5x10-6m/2x10-6
m1 14.40 m2 300 m3 48.60 m4
900 not visible
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Thin Film Interference
Let film thickness t
Assume no net phase change on reflection
2t ml m0, 1, 2 Condition for bright
2t (m1/2) l Condition for dark
For one hard reflection 2t ml becomes condition
for dark
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Complication 1Soft and Hard Reflections

• SOFT
• beam exits higher n material
• No phase shift on reflection

• HARD
• beam enters higher n material
• Phase shift of l/2 on each reflection

Air n1.0
Coating n1.38
Glass n1.52
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Complication 2What Wavelength to Use

• Use ln l/n where n is the index of refraction
  in the medium where refraction occurs (the film)
• Example green 500nm light leaves air and enters
  a thin layer of oil n1.25 floating on water.
  What wavelength should be used to find the
  minimum thickness of oil for the oil to appear
  green?

ln l/1.25 500nm/1.25 400nm
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Oil On Water
How many hard reflections are there? What is the
total phase shift due to reflections?
1
l/2 180
What l should you use?
ln l/1.50
Courtesty of http//physics.bu.edu/duffy/PY106/Di
ffraction.html
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What Really Happens
This shows why the wavelength must be divided by
n in the film to get the two reflected waves to
interfere completely destructively
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Anti-reflective Coating
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Problem

• A coating of MgF on glass has an index of
  refraction of 1.38. What is the minimum
  thickness of this coating to prevent reflection
  of 550 nm light?

2t (m1/2) ln For m 0 t ln/4
tl/1.38/4
t 100nm
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Puzzle

• If the two reflected beams interfere
  destructively, what happens to their energy?

It is transmitted! Thats the point of an
antireflective coating.
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Multi Coating
Super-Multi-Coating (SMC) - Pentax's unique seven
layer coating applied to each lens element of the
lens to increase light transmission, increase
color saturation and to help prevent flare.
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Polarization

• Intensity varies as polarizer is rotated

Courtesy Siltec Ltd.
39
Polarization
In linear Polarization light vibrations become
confined to a single linear plane
Courtesy of 3M Corporation
40
Polarization Analogy
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Two Polarizers

• What will happen if the polarized beam hits
  another polarizer rotated 900 from the first?

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Propagation of a Linearly Polarized
Electromagnetic Wave
Animation Courtesy Siltec Ltd. http//www.infoline
.ru/g23/5495/Physics/English/feedback.htm
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Courtesy http//webug.physics.uiuc.edu/courses/ph
ys112/summer97/lectures/lect24/sld014.htm
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n c/v
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Link to Interference Applet

• In ripple tank
• link