Thin Film Interference

Interference + Light

Superposition

t

+1

-1

t

+1

-1

t

+2

-2

+

Destructive Interference

Out of Phase180 degrees

Superposition

t

+1

-1

t

+1

-1

t

+2

-2

+

Constructive Interference

In Phase

Electromagnetic Waves

• Light, Radio, TV, Microwaves, Satellites, X-Rays

Electromagnetic Waves

xz

y

• Transverse (vs. sound waves – longitudinal)• E perpendicular to B and always in phase

E & B increase and decrease at same times• Can travel in empty space (sound waves can’t!) • “Speed of light”: v = c = 3 x 108 m/s (186,000 miles/second!)• Frequency: f = v/= c/Period: T = 1/f

wave travels one wavelength in one period T

vcn

Speed of light in medium Index of

refraction

Speed of light in vacuum

n1 v c so

Index of Refraction186,000 miles/second: it’s not just a good idea, it’s the law!

always!

In general n increases with density of the medium.

Index of Refraction1. Speed changes when moving to

a new medium.2. Frequency of the light remains

constant.3. Therefore, the wavelength

changes. vold f *old and vnew f

*new

vnew / vold newold nold /nnew = newold

Thin Film Interference

n1 (thin film) n2

n0=1.0 (air)

t

1 2

Get two waves by reflection off two different interfaces.

Ray 2 travels approximately 2t further than ray 1. 37

Reflection + Phase Shifts

n1

n2

Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change.

• If n1 > n2 - no phase change upon reflection.• If n1 < n2 - phase change of 180º upon reflection. (equivalent to the wave shifting by /2.)

Incident wave Reflected wave

39

Thin Film Summary

n1 (thin film) n2

n = 1.0 (air)

t

1 2

Ray 1: 1 = 0 or ½

Determine number of extra wavelengths for each ray.

If |(2 – 1)| = ½ , 1 ½, 2 ½ …. (m + ½) destructive

If |(2 – 1)| = 0, 1, 2, 3 …. (m) constructive

Note: this is wavelength in

film! (film= o/n1)

42

+ 2 t/ film

Reflection Distance

Ray 2: 2 = 0 or ½+ 0

This is important!

Thin Film Practice

nglass = 1.5

nwater= 1.3

n = 1.0 (air)

t

1 2

Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither?

45

1 = 0 B) 1 = ½ C) 1 = 1What is 1, the total phase shift for ray 1

Thin Film Practice

nglass = 1.5

nwater= 1.3

n = 1.0 (air)

t

1 2

Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither?

45

Thin Film

nglass =1.5

nplastic=1.8

n=1 (air)

t

1 2

Blue light = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: (A) constructive (B) destructive (C) neither

48

The gas looks: • bright• dark

A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength…

t =

nwater=1.3

ngas=1.20nair=1.0

noil=1.45

The oil looks: • bright• dark

50

Thin Film Practice

nglass = 1.5

nwater= 1.3

n = 1.0 (air)

t

1 2

Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither?

45

Thin Film Practice

nglass = 1.5

nwater= 1.3

n = 1.0 (air)

t

1 2

Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither?

45