# Thin Film Interference

Ever looked at a soap bubble and wondered why there where colors in it? Why do they change as the bubble moves? What's the shimmering when there is a film of oil on water? These colors and patterns are due to a phenomenon known as Thin Film Interference. In order to establish Thin Film Interference, we want to review two important properties of waves.

1. The first property deals with reflection: When a wave strikes the surface of another medium, a portion of the energy of that wave is reflected back. If the optical density (or index of refraction) of the second medium is greater than the optical density (or index of refraction) of the first medium, then the reflected wave exhibits a phase shift of 180o.

2. The second property is that the portion of the wave that passes through the second medium will be refracted in accordance with Snell's Law. Remember that, even though the speed of the wave changes in the second medium, the frequency remains the same and so the wavelength must also change.

Let us suppose that white light strikes an air/oil/water interface, such as we might get on a puddle.  Per the diagram on the right (and I'm really going to simplify this), we can see that some light gets reflected at Point A, the air/oil surface. But some light will pass through and some of that will be reflected again at point B, the
oil/water interface. That reflected light will travel back to the surface and be refracted again as it leaves the oil and enters the air. Now, some important things happen:

• White light is made up of wavelengths of light from 400 - 750 nm.
• Since the air/oil interchange represents reflection from a denser medium, the surface reflected light undergoes a phase change and is shifted 180o.

• Since the oil/water interchange does not represent reflection from a denser medium, the second reflected light will not be phase shifted.
• If the total path length from A - B - C equals a half of a wavelength that falls within the visible light spectrum, then that particular ray will be in phase with the surface reflected ray and there will be constructive interference. That color becomes visible on the surface. The thickness of the film (oil) must equal a quarter of the wavelength (half of the path length) in order for there to be constructive interference.
• There will be another ray (not shown) that reflects of the bottom of the water. This ray will provide yet another path length difference and another color that may be viewed.

The angle of viewing changes the path length, as does the thickness of the film. Figuring out the Path length difference that the surface reflected ray takes and the internal reflected ray can determine the thickness of the film that will cause a particular wavelength of light to be reflected.

Follow these links to see what other people have to say on the subject:

http://physics.bu.edu/py106/notes/Thinfilm.html

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/soapfilm.html

http://online.cctt.org/physicslab/content/PhyAPB/lessonnotes/twosourceinterference/thinfilminterference.asp

http://www.physicsclassroom.com/Class/light/u12l1c.html

For Practice Problems, Try: Giancoli Multiple Choice PracticeQuestions (Questions 1-21)