# Thin Film Interference

Interference patterns seen in thin films

If a thin oil film is floating on the water, you will see a beautiful pattern appear on the oil film.
This is because the two waves interfere with each other. One wave is reflected from the surface, and the other is reflected from the inside.

Rainbow colors are common in soap bubbles. The difference from the rainbow in the sky is that the bands of color tend to repeat.

The principle of the interference pattern generated

As shown in the figure below, when one strand of light enters the soap film, two branched reflections occur.

If the two phases can merge with each other, it look bright (reinforcement interference).

If the two phases cancel each other out, it looks dark (offset interference).

Visible light has different wavelengths depending on the color of light.That is, red light has a wavelength of about 600 nm, blue light has a wavelength of about 450 nm.Depending on the thickness of the film, the wavelength at which reinforcement interference occurs will continue to vary. This is why thin films look colorful.

The light intensity of the interference pattern

Bright condition   $$2nL\, =\, (m+\frac { 1 }{ 2 } )\lambda$$
Dark conditions   $$2nL\, =\, m\lambda$$

m = 0, 1, 2, ... A value indicating how many times the thickness of a bubble is the wavelength of light
n: Refractive index of soapy water
L: Bubble thickness (nm)
λ: Wavelength of light (nm)