COHERENCE, INTERFERENCE,

AND THIN FILMS

Purdue University – Physics 241 – Lecture 26 Brendan Sullivan

Overview

Wave superposition

Constructive vs. deconstructive interference

Wave phases

(Optical) Path length difference

Reflection Boundary Conditions

Thin film interference

Young’s double slit experiment

Wave superposition is merely the

addition of waves

-3

-2

-1

0

1

2

3

0 1 2 3 4 5 6 7

Constructive (in-phase) interference –

blue+orange = green

-1.5

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4 5 6 7

Deconstructive (out of phase) interference

– blue+orange = green

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8

Arbitrary wave addition (superposition) -

blue+orange = green

0GreenBlue

180GreenBlue

Path length difference leads to a

difference in phase for waves

Consider two waves that

start at the same phase,

but have to travel

different distances

While the wave is

moving, its “current

phase” is changing

If the waves travel

different distances, then

their phases have

changed relative to

eachother

2360rr

Light reflecting of optically denser

material picks up 180° phase change

If n2>n1 we pick up 180°

phase change

Comes from boundary

conditions of wave equation

Similar to a guitar string

reflecting off bridge

This plays a role in

determining if waves will

constructively or

deconstructively interfere

n=1

n>1

180° phase change

No 180° phase change

Thin film interference

“Thin”: A couple of wavelengths

of light

Condition for maximum (bright

fringe): The two reflected

waves interfere constructively

Minimum: deconstructively

Example: Air, soap, air bright

fringes

mt2Maxima:

Minima: )2

1(2 mtn

air

Thin films exhibit either our answer or

the opposite

We had n2>n1 and n2>n3. If we have an intermediate index of refraction (e.g. n1>n2 and n3>n2) then the 180° phase change gives us the opposite answer

The equations fail for some of the following situations. Which one(s)?

Glass wedges act like thin films of

varying thickness

Two pieces of glass

ramped (like at right) act

like a thin film

We’ll do an example

Newton’s Rings: the air

between the glass plates

acts like a thin film

Newton’s Rings

• Since the thickness of the film changes over the radius of the

plates, alternating bright and dark fringes form, when the

plates are illuminated. Because of the curvature of the upper

piece, the film thickness varies more rapidly at larger radius.

Thus the fringe separation is smaller toward the outside.

The double slit pattern is a result of

constructive interference

Double slit experiment: two small

slits act as point light sources

We observe their interference

pattern on a screen a distance L

away

Bright fringes: constructive

interference

Dark fringes: deconstructive

interference

md )sin(

)2

1()sin( md

Determining the intensity of fringes

For two coherent EM waves:

The overall field thus is:

We showed that intensity is

proportional to E2:

1 0

2 0

sin

sin( )

E E t

E E t

1 2

0

0

sin sin( )

2 cos sin2 2

E E E

E t t

E t

2

0 0

2

024 cos

2

m II E

I EI

2)sin(d

This is the phase

difference between the

two rays

m is simply an index for the extremal

points

2

04 cos2

I