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6.2 Two slit interferenceCoherence
Two-Slit Interference
Thin film Interference
Interference Effects
Interference is a general property of waves.
A condition for interference is that the wave source is coherent.
Interference between two waves gives characteristic interference patterns due to constructive and destructive interference.
Coherence
For two waves to show interference they must have coherence.
Two waves are coherent if one wave has a constant phase relation to the other
coherent incoherent
phaseshift
x2
Coherence
Light fromtwo separatelight bulbs isIncoherent
Light from a singlelight bulb passingthrough two slits iscoherent
Interference
=0
Sum
Constructive Interference
Interference
= 2
Destructive Interference
Interference
= Constructive Interference
path difference
path difference = =r2 – r1
In phase
Condition for constructive interference m
Condition for destructive interference1
( )2
m
m = 0 + 1, + 2,….
r1
r2
Superposition of wavesat A shows interferencedue to path differences
A
Order number m
Interference pattern of water waves
Constructive
Destructive
Interference pattern due totwo spherical waves
Coherent waves
Interference pattern
Amplitude on screen
=0
=
=-
m=0
m=1
m=-1
Young’s two slit experiment
Thomas Young
Does light show wave properties?
Path difference from the two slits
path difference dsin
In the limit L>>d, the rays are nearly parallel
Interference pattern
Bright constructive interference brightdsin m
Darkdestructive interference darkdsin (m 1/ 2)
m = 0, + 1, + 2, ............
d m=0m=1
m= -1
maxima
m= -2
m=2
Central maximum
QuestionLight from a laser is passed through two slits a distance of
0.10 mm apart and is hits a screen 5 m away. The separation between the central maximum and the first bright interference fringe is 2.6 cm. Find the wavelength lf the light.
for m= 1
2 37yd (2.6x10 )(0.1x10 )
5.2x10 520nmmL (1)(5)
dsin=m sin ~ y
L
for smallangles
yd m
L
solve for
L
yd
Clicker Question 1
In a two slit interference experiment, how does the separation between peaks in the interference pattern change if the distance between slits is increased?
A. Increase
B. Decrease
C. Stays the same
D. Indeterminate
Clicker Question 2
In a two slit interference experiment how does the distance between the peaks on the screen change if the wavelength of the light is increased?
A. increases
B. decreases
C. stays the same
D. indeterminate
Thin film interference
• In thin film interference the phase difference is due to reflection at either side of a thin film of transparent material.
• The phase difference is due to two factors:– Path difference through the film (corrected for the
change in speed of light in the material)– Phase shift due to reflection at the interface
Phase shift due to reflection
n1 < n2
phase shift=180o
Reflection with inversionphase shift = 180o
Phase shift due to reflectionReflection without inversionPhase shift = zero
n1 > n2
Phase shift = zero
Thin film Interference
For a thin film in air the phase difference due toreflection is 180o
Condition for constructiveinterference
=2t= film
1 1(m ) (m )
2 2 n
The wavelength in the film is longer than in air.
Thin film Interference
For film in air the phase difference due toreflection is 180o
Condition for destructiveinterference
=2t= filmm mn
The wavelength in the film is longer than in air.
Soap film interference pattern
Soap film
Question
A vertical soap film displays a series of colored band due to reflected light. Find the thickness of the film at the position of the 5th green band (=550 nm, n =1.33)
Constructive Interference The 5th band has m=4 (the first is m=0)
12t (m )
2 n
1t (m )
2 2n
971 550x10
(4 ) 9.3x10 m 930nm2 2(1.33)
Anti-reflective Coating
Anti-reflective coatings are usedto reduce reflections at the air-glassinterface.
anti-reflectivecoating
no coating
Anti-reflective CoatingAnti-reflective coatings consists of a thin-layer of material with a refractive index in between that of air and glass. Destructive interference between light reflected at the two surfaces reduces the intensity of reflected light.
n1=1.00 < n2 < n3 Condition for destructive interference.
2
12 ( )
2 t m
n
t
n1 n2
n3
phase shift of 180o atboth interfaces.Total phase difference due to reflection is zero
QuestionAn anti-reflective coating of MgF2 (n=1.38) is used
on a glass surface to reduce reflections. Find the minimum thickness of the coating that can be used for green light (=550 nm).
For destructive interference
12
2t
n
4tn
550100
4(1.38)nm
Quarter wavelength (in coating) thickness
2
12 ( )
2 t m
n
minimumat m=0
Solve for t
Optical compact disc
Cd store information in a seriesof pits and bumps in the plastic.The information is read by a reflectedlaser beam. The intensity of the beam is changed byconstructive or destructive interference
4tn
destructive interference