The Wave Nature of Light Thin Film Interference. Objectives, you should be able to: 1.Understand the principles of refraction 2.Apply the principles of.

The Wave Nature of Light Thin Film Interference

Objectives, you should be able to:

1.Understand the principles of refraction

2.Apply the principles of interference to light reflected by thin films

Thin Film Interference• Interference also occurs as waves travel through

different media. • If there is a very thin film of material – a few

wavelengths thick or less – light will reflect from both the bottom and the top of the layer, causing interference.

• Examples: soap bubbles and oil slicks

Refraction (Bending) of Waves

Waves propagate more slowly in the medium of higher index of refraction. This leads to a bend in the wavefront.

The frequency of the light does not change, but the wavelength does as it travels into a new medium.

The index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium:

Index of Refraction

vc

n

n1 v c soalways!

Thin Film Interference

n1 (thin film)

n2

n0=1.0 (air)

t

1 2

Get two waves by reflection off of two different interfaces.

Ray 2 travels approximately 2t further than ray 1.

Constructive interference: wave that travels through the film & back must have traveled just the right distance such that it is in phase

*Film thickness must be on the order a few or less

Thin Film Interference• In addition to thickness of film

(distance)– light reflects off a surface of higher

index of refraction, a 180° phase shift occurs (n1<n2)

• Light in air reflecting off just about anything (glass, water, oil, etc.) will undergo a 180° shift.

– When n1>n2, no phase shift occurs• light in oil, which has a higher n than

water does, will have no phase shift

– Note a shift by 180° is equivalent to the wave traveling a distance of half a wavelength.

Constructive Interference:Phase shift at surface ½, reflection from oil/water no phase shift and travels ½ [If film thickness was ½ , then travel 1 and would be destructive (off by ½ )]

Destructive Interference:Phase shift at air surface, reflection from coating/lens phase shift ½ and travels ½ (off by ½ ) (If film thickness was ½ , then travel 1 and would be constructive)

Non-reflective coatings

Constructive or Destructive

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)+ 2 t/ film

Reflection Distance

Ray 2: 2 = 0 or ½

This is important!

Thin Film Practice

nglass = 1.5

nwater= 1.3

n = 1.0 (air)

t

1 2

1 = ½

2 = 0 + 2t / glass = 2t nglass/ 0= 1

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?

Phase shift = 2 – 1 = ½ wavelength

Reflection at air-film interface

Equations for Thin Film Interference (if you an equation kind-of person)

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=1.20

nair=1.0

noil=1.45

1,gas = ½The oil looks: • bright• dark

2,gas = ½ + 2

1,oil = ½ 2,oil = 2

|2,gas – 1,gas | = 2

| 2,oil – 1,oil | = 3/2

constructive

destructive

Different colored lines• different locations of the film may be of

appropriate thickness to reinforce different colors of light (different )

BRIGHT

BRIGHT

DARK

0 t 2λ

t λ t

m =1 m =2 m =3

DARK

DARK

Interference by Thin Films

One can also create a thin film of air by creating a wedge-shaped gap between two pieces of glass.

Newton’s Rings• interference is seen when a planoconvex

lens is placed on top of a flat glass surface• The air film between the glass surfaces

varies in thickness from zero at the point of contact to some thickness t

• A pattern of light and dark rings is observed– This rings are called Newton’s Rings– The particle model of light could not explain the

origin of the rings

An antireflective coating (n=1.38) is coated on a plastic lens (n=1.55). It is desired to have destructive interference for =550nm (center of visible spectrum). What is the thinnest film that will do that?

1. How many phase changes? (air-film-glass)2 (both surfaces low to high n)

2. Equation for destructive for 2 phase changes

3. Solve for t (m=0 for thinnest)2nt = (m + ½ ) λ

t = (m + ½ ) λ / 2nt= ½ (550) / 2 (1.38) = 99.6 nm

Interference by Thin Films

Problem Solving: Interference

Interference occurs when two or more waves arrive simultaneously at the same point in space.

Constructive interference occurs when the waves are in phase.

Destructive interference occurs when the waves are out of phase.

An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.