# Document ```Chapter 27
Physical Optics
Interference and the Wave Nature of Light
0. Waves
• Disturbance propogating through space
1. Linear Superposition
Resultant disturbance from 2 waves is sum of
individual disturbances
a) Constructive Interference
(b) Destructive interference
2. Young’s Double Slit, 1801
- the first definitive evidence of the wave-nature of light
a) The phenomenon
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b) The concept
c) The equation
When l  m  constructive interference (m  0,1,2...)
When l  (m  1 2)  destructive interference (m  0,1,2...)
From the geometry, l  dsin , so
m  dsin   bright fringe

(m  12)  dsin   dark fringe
m  dsin   bright fringe
(m  12)  dsin   dark fringe


White light interference
3. Thin film interference
a) The phenomenon &amp; concept
• 1, 2 travel different paths
• interference possible
• depends on wavelength (color)
• depends on thickness (pattern)
• depends on angle (pattern)
b) The equations
Constructive Interference:
(Eff. path length)  m
Destructive Interference:


(Eff. path length)
 (m  12)
Contributions to Eff. path length:
(i) Geometrical path length = 2t
(ii) Optical path length
OPL = eq’t distance traveled in vacuum
For distance 2t,
2t c2t
OPL  c 
 2nt
v c /n
Or use wavelength in medium:


 film  vacuum
n
(iii) Phase change for increasing n




2
(Eff. Path Length)
= OPL 
EPL = 2n filmt 


2

2
(one phase change)
(one phase change)
Constructive Interference:
EPL  m
1
EPL

(m

Destructive Interference:
2)


4. Michelson Interferometer
• Used to measure wavelength
If DA  DF , constructive interference
If DA  DF   4 , destructive interference
If DA  DF  m 2 , constructive interference
• Adjust DA by measured amount (y)
and count (N) bright-dark cycles:
y

2N
5. Diffraction
a) Huygen’s principle, 1678
Every point on a wave front acts as a source; the
advancing front is the sum of waves from each source.
Effectively, the tangent of the point-source waves forms
b) Diffraction phenomena
Waves bend around obstacles.
Depends on ratio:

W

W
Diffraction pattern observed
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c) Equation for minima
Bright fringe at  = 0
First dark fringe
sin  


W
1, 3 cancel
2, 4 cancel
Each ray in upper half
cancels a ray in lower
half
Second dark fringe
2
sin  
W

Equation for dark fringes:
Each ray in 1st quarter
cancels a ray in the
second quarter; each ray
in the 3rd cancels one in
the fourth.
m  W sin 
Diffraction pattern: Central fringe is brightest because all rays
interfere constructively.
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Example:
Problem 27-27
Width of central fringe is 450 times slit width. Find
W if the distance to the screen is 18000W.
6. Resolving Power
a) The concept
Diffraction at the apertures in optical instruments
(pupil), limit resolving power.
b) Diffraction at circular aperture
sin   1.22

D
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
D
c) Rayleigh Criterion
Objects resolved when first dark fringe of one
coincides with the central bright fringe of the other
 min  1.22

D
Example: Human and Eagle eyes
(a) Find minimum s for
human (D = 2.5 mm)
(b) Find minimum s for
eagle (D = 6 mm)
d) “Absurd” diffraction around a circular obstacle
In 1818, the young Fresnel entered his wave theory in
Poisson, one of the judges, predicted a bright spot at
the centre of the shadow of a disc, based on Fresnel’s
theory.
“Such an absurdity must surely disprove the entire
theory!”
Arago, another judge, went to the laboratory, and saw
the absurd. … paraphrased from Hecht, Physics
Diffraction around a
pushpin
image
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pin
Laser
7. Diffraction grating
a) 2-slit interference
m  dsin 
for maxima
(m  1 2)  d sin 
for minima
(b) 3-slit interference
For (m  12)  dsin  adjacent slits cancel
y1  sin( x)


m  dsin 
for principal maxima



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y2  sin( x   )
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y3  sin( x  2 )
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y  y1  y2  y3
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Resultant is not zero.
Complete cancellation occurs when waves are offset by 3.
--&gt; 2 minima between principal maxima:
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(c) N-slit interference (diffraction)
4 slits
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5 slits
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50 slits
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(d) Separating colors
m  dsin 
for principal maxima

(e) The grating spectroscope
(f) Diffraction patterns to probe structure
Examples:
- difference in diffraction angles from CDs and DVDs
- diffraction pattern to determine thickness of hair
- diffraction pattern from complex gratings (textiles etc)
- principle of holography
8. Interference and optical media
Pit thickness t = 4
giving destructive
interference in beams
reflected from edges.
Variation in intensity used
Two tracking beams
produced by a diffraction
grating are used to