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