Thin Film Interference

What is a thin film?

A thin film is a thin layer of material that has a different index of refraction than its surroundings.

Thin films cause incident light to undergo interference (constructive or destructive, depending on the wavelength of the light and the thickness of the film).

Thin film interference is responsible for all of the colors that appear in soap bubbles and oil slicks.

When light is incident on a thin film,

part of the incident light is reflected off of the top of the film, and part is transmitted into the film and reflected off of the bottom!

t = thickness of the film

air

soap

air

incident ray

refle

cted

ray

1

refle

cted

ray

2

It is the interference of these two reflected rays that we will see when we look into the film.

t

incident ray

refle

cted

ray

1

refle

cted

ray

2

refle

cted

ray

4

refle

cted

ray

3

In reality, the light makes many, many reflections in the film!

However, we only need to analyze the first two reflected rays in order to make predictions about the interference pattern.

There are two types of thin films

low n

low n

high n

low n

higher n

high n

air

soap

air

air

oil

ground

Type I: Oil slick type (fast-slow-slower)

Type II: Bubble type (fast-slow-fast)

Type I: Oil Slick Type

air(n = 1.0)

oil(n ≈ 1.5)

ground(very high n)

t

1 2

Light is incident upon the oil from the air. It is partially transmitted into the oil, and partially reflected back into the air.

The light in the oil reflects off of the ground, and refracts back out into the air.

As a result, we have multiple rays coming toward our eyes that started from the same incident ray!

The most important concept of thin film inteference

air(n = 1.0)

oil(n ≈ 1.5)

ground(very high n)

t

1 2

If rays 1 and 2 are in phase with one another, then there will be constructive interference. You will be able to see that wavelength of light from the surface of the film.

If rays 1 and 2 are out of phase with one another, then there will be destructive interference. You will not be able to see the wavelength of light from the surface of the film.

air(n = 1.0)

oil(n ≈ 1.5)

ground(very high n)

t

1 2

The waves start out in phase, but travel different path lengths by the time that they are superimposed

Wave 2 travels an extra distance of ≈ 2t!

However…

air(n = 1.0)

oil(n ≈ 1.5)

when a wave (even light) is reflected off of a different medium, it may invert, depending on the density of the medium! Let’s review how this works.

Boundary Reflections: Revisited

When a wave reflects off of a more dense medium than the one in which it is traveling, it will become inverted.

This is called a 180° phase change.

Less dense

More dense

This same principle applies to light reflecting off of a medium with a higher refractive index.

180° phase flip – trough becomes a crest, or vice versa

Type I Thin Films: Oil Slick

air(n = 1.0)

oil(n ≈ 1.5)

ground(very high n)

t

1 2

At which interface(s) does the reflecting light undergo a phase flip?

air(n = 1.0)

oil(n ≈ 1.5)

ground(very high n)

1 2

At which interface(s) does the reflecting light undergo a phase flip?

At both!

When the light reflects off of the oil from the air, it is phase

flipped.

When the transmitted ray reflects off of the ground at

the bottom of the oil, it is also phase flipped!

Since both of the waves that are interfering have undergone a 180° phase flip, the net result is the same as if neither of the waves did!

A summary so far

air(n = 1.0)

oil(n ≈ 1.5)

ground(very high n)

t

1 2The waves start out in phase.

Both parts undergo phase flips at some point (so it is mathematically the same as if neither one did).

Wave 2 travels an extra distance of ≈ 2t

And now for the grand finaleThe waves started out in phase, but one of them went some extra distance.

In order for them to constructively interfere, they must be back in phase when they are superimposed.

Does this sound familiar?

Constructive interference must satisfy the equation

m = 0 if the waves have traveled the same distance, m = 1 if one of the waves has traveled one extra wavelength, m = 2 if one of the waves have traveled two extra wavelengths, etc.

Where L1 is the distance traveled by the wave reflected off of the top of the film, and L2 is the distance traveled by the wave reflected off of the bottom of the film

The end result!

t

1 2

Wave 2 has traveled an extra distance of ≈ 2t.

This gives the end result

for constructive interference in a type I thin film.

And, for destructive interference…

in a Type I thin film (low-high-higher)