# 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
between tracks.
9. X-ray diffraction
Regular arrays of atoms
produce diffraction
patterns, for short
This diffraction pattern produced
by Rosalind Franklin in 1953 helped
determine the structure of DNA.
The method is used routinely for structural determination.
```