Physical Optics. Diffraction.
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Interference
Young’s interference experiment
Thin films
Coherence and incoherence
Michelson interferometer
Wave-like characteristics of light
Huygens-Fresnel principle
Interference.
Interference = superposition of two (or more) coherent waves
that results in a new wave pattern.
Coherent = same frequency
Examples. (from Phys 213)
1. Standing waves = incident wave + reflected wave
2. Two identical sound sources
Young’s Double Slit Experiment. Qualitative.
To see if the light interferes, we pass it subsequently
through two separated slits and see if an interference
pattern is produced
screen
This is an
interference
pattern!
Where crests from S1 and
crests from S2 meet at the
screen, a bright fringe
appears. Where crests
and troughs meet, a dark
fringe appears.
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Young’s Double Slit Experiment. Experimental.
Example of an
interference pattern
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Young’s Double Slit Experiment. Quantitative.
Basic idea: waves from each slit will, in general, travel different distances to a given
point on the screen
if they arrive perfectly in phase, they constructively interfere, i.e., they add to one another:
bright fringe
if they arrive perfectly out of phase, they destructively interfere (as shown below): dark
fringe
if they arrive in between, they do a little of both: part of fringe pattern in between bright and
dark fringes
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Young’s Double Slit Experiment. Quantitative.
Constructive interference
∆L = dsinθ
θ = mλ, m=0,1,2,..
(bright fringes)
Location on the screen
Question: what happens to the interference pattern
if we use green laser light instead of red?
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Young’s double slit experiment. Sample Problem.
Monochromatic green light, wavelength
550 nm, illuminates two parallel narrow
slits 7.7µ
µm apart. Calculate the angular
deviation θ of the third-order (m=3) bright
fringe in radians and degrees.
www-viz.tamu.edu
The colors seen
in a soap bubble,
or from some oil
spilled on the
ground, are due
to interference
effects
physics.utoledo.edu
Thin Film Interference
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Thin Film Interference
• On reflection, waves may
experience a phase shift of π or λ/2
• Example: pulses on strings
a) denser
lighter (slower
faster):
no shift
b) lighter
denser (faster
slower):
λ/2 shift
Constructive interference (bright)
2Ln2/cosθ = m+½ , m=0,1,2,…
Destructive interference (dark)
2Ln2/cosθ = m, m=0,1,2,…
air soapfilm air
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Thin Film Interference. Sample problem
Monochromatic light of λ=624nm is
incident perpendicularly on a soap film
with n=1.33, suspended in air.
What are the least two thicknesses of the film
for which the reflections from the film
undergo fully constructive interference?
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Thin Film Interference. Sample problem
Monochromatic light of λ=400 nm is
incident perpendicularly on a soap film
with n=1.33, covering glass (n=1.8).
What is the least thickness of the film for
which the glass is invisible?
Can we apply that to “stealth” technology?
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Thin Wedge Interference
A broad beam of light of wavelength 623 nm is sent directly
downward through the top plate of a pair of glass plates. The
plates are 120 mm long, touch at the left end, and are separated
by a wire of diameter 0.048 mm at the right end. The air
between the plates acts as a thin film. How many bright fringes
will be seen by an observer looking down through the top plate?
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Coherence and Incoherence
• You may have noticed that in
the Young’s double slit
experiment, there was a single
slit in front
• But when I used the laser—or
the microwave—apparatus,
this single slit was not needed,
and yet the interference
patterns were essentially the
same in all cases
Coherence and Incoherence
• The reason is that Young had to use sunlight
sunlight is incoherent light, meaning that the phase
difference between the light waves at any two points in space
is not constant over time
• it is nearly constant at small distances, but not constant over
distances comparable to “d” the distance between the double-slits
if incoherent light is sent through the double slits, the
interference pattern would not be seen
• the first slit in the Young’s experiment insures that the light that hits
the double slits hits each slit with the same relative phase
• We got around this problem by using a coherent
emitter of radiation, namely the laser (or the klystron
that emitted the microwaves)
For incoherent sources intensities add up not field amplitudes!
(recall unpolarized light and polarizers)
Michelson Interferometer
1852-1931
First to measure speed of light
(with high precision, 1879)
First American Noble Prize
winner (1907)
Permits measurements of distances as small as a fraction of the wavelength of
light used
Principle of operation:
• light from source S goes to partially silvered mirror, M
transmits some of light, reflects rest
• light goes to mirror M1 or M2, and back to M, traveling distances 2d1 and 2d2,
respectively
• these two light waves interfere and this interference pattern is seen by the observer
• if one mirror (say M2) is moved by l/4, the observer will see (say) a dark fringe
change into a bright fringe
Applications: LIGO! (recitation)
Huygens-Fresnel principle.
1629-1695
1788-1827
“Each point reached by a wave
acts as a (point) source of secondary waves”
“New wavefront is the result of
interference of the secondary waves”
Later supplemented by Kirchhoff (1824-1887)
(Phys 212 fellow)
Huygens-Fresnel principle.
Propagation of light
Refraction of light
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Recap
• Thin films-bright
2L = (m+½)(λ/n)
• Thin wedge - # fringes
m=[2Ln/ l -½]
• Double Slit-bright
∆L = dsinθ = mλ
• Michelson Interferometer
Shift one mirror arm, see change in fringes
Next Time
• Diffraction
Quantifying single slit diffraction
Intensity in single slit diffraction
circular aperture diffraction
double slit diffraction
• Diffraction gratings