Thin Film Interference II

Thin Film Whiteboard I!White light is incident upon a type I thin film from above, as shown below. Then, the thickness of the film is steadily decreased. At the thickness of the film approaches zero, what will you see when looking at the film?

white light

a) The film would appear bright.b) The film would appear dark.c) It depends on the wavelength of light used. air

(n = 1.0)

oil(n > 1.0)

ground(very high n)

air(n = 1.0)

oil(n > 1.0)

ground(very high n)

1 2

Both reflected rays undergo a phase shift, so it is the same as if neither one did!

12

As the thickness of the film approaches zero, |L2 – L1| approaches zero.

(The second ray does not travel any further than the first if t = 0)

If the rays are in phase, and are immediately superimposed, they will cause the film to appear bright.

(constructive interference)

For a Type I thin film, constructive interference will occur if the following relationship is satisfied

Red light has the longest wavelength, so it will

constructively interfere on the thickest part of the film.

Violet light has the shortest wavelength, so it will

constructively interfere on the thinnest part of the film.

Then green…

The m = 1 spot will exist when ray 2

goes one wavelength further than ray 1

This also means that at different thicknesses of the film, different m values for the same color will be satisfied.

The m = 2 spot will exist when ray 2 goes

two wavelengths further than ray 1

The m = 3 spot will exist when ray 2 goes

three wavelengths further than ray 1

0.5λ 0.5λλ λ

1.5λ 1.5λ

Type II: Bubble Film Type

air(n = 1.0)

soap(n ≈ 1.3)

t

1 2

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

The light in the soap reflects off of the bottom of the soap film, and partially refracts back out into the air.

air(n = 1.0)

Type II Thin Films

air(n = 1.0)

soap(n ≈ 1.3)

t

1 2

air(n = 1.0)

Ray 1 reflects off of a more dense medium at the top of the film.

Ray 2 reflects off of a less dense medium at the bottom of a film.

When a wave reflects off of a less dense medium than the one in which it is traveling, it will not become inverted.

The same rule applies to light!

If the light wave reflects off of a less dense medium (lower n), the wave will not become inverted.

soap(n = 1.3)

air(n = 1.0)

air(n = 1.0)

soap(n ≈ 1.3)

1 2

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

Only at the top!

When the light reflects off of the soap from the air, it is

phase flipped.

When the transmitted ray reflects off of the air at the bottom of the film, it is not

phase flipped.

Since only one of the waves that are interfering have undergone a 180° phase flip, the net result is for two sources are out of phase

air(n = 1.0)

For two out of phase sources, constructive interference must satisfy the equation

Note: This is the opposite as for a Type I thin 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 II thin film.

And, for destructive interference…

in a Type II thin film (low-high-low)

Thin Film Whiteboard II!White light is incident upon a type II thin film from above, as shown below. Then, the thickness of the film is steadily decreased. At the thickness of the film approaches zero, what will you see when looking at the film?

white light

a) The film would appear bright.b) The film would appear dark.c) It depends on the wavelength of light used. air

(n = 1.0)

soap(n = 1.3)

air(n = 1.0)

Thin Film Interference: SummaryType I Thin Film Type II Thin Film

air(n = 1.0)

oil(n > 1.0)

ground(very high n)

low

high

higher

air(n = 1.0)

soap(n = 1.3)

low

high

lowair

(n = 1.0)

Constructive Interference

Destructive Interference

Constructive Interference

Destructive Interference

air(n = 1.0)

oil(n > 1.0)

1 2

Only one of the reflected rays undergo a phase shift, so the film behaves like two out of phase sources!

12

As the thickness of the film approaches zero, |L2 – L1| approaches zero.

(The second ray does not travel any further than the first if t = 0)

If the rays are out of phase, and are immediately superimposed, they will cause the film to appear completely dark.

(destructive interference)

air(n = 1.0)

Final Whiteboard Question

A camera lens with an index of refraction of 1.67 is coated with an anti-glare thin film that has an index of refraction of 1.82.

What must be the thickness of the film if its purpose is to destroy yellow light (wavelength 580 nm)?

Draw a picture to determine which type of thin film this is!