Light in a vacuum always travels at a speed c = 2.99 x 10⁸ m/s. When any wave is incident on a boundary, like when light travels from the air onto water, some of the wave is reflected and some of it is transmitted. Experiment will show that light appears to slow down while traveling through the water as opposed to the air. This is called the effective speed (veffveff) of the light in the medium. The Index of Refraction (n) is a measure of the effective speed of light in a medium.

n=cveffn=cveff

Notice, that since nothing can travel faster than the speed of light, that the index of refraction is always greater than or equal to 1. This slowing down of light also causes the wavelength to change.

This is because the constant for a wave across a boundary is the frequency. with v=fλv=fλ, if the frequency is constant and the speed decreases, the wavelength must also decrease. You'll also notice the direction the light travels also changes. The index of refraction can be used to determine how much light bends when traveling from one medium to the next. See Snell's Law of Refraction for more about the bending of light.

When light is incident on a boundary where the index of refraction is changing, some of the light is reflected and some of that light is transmitted. This can have interesting effects when light is incident on a very thin film of certain materials. Consider the situation below, which could represent oil on top of water. Air would be the top surface, oil would be the thin film, and water would be the bottom surface.

Here light ray (1) is the original light beam incident on the top interface. It splits into two rays - (2) is the reflected ray and (3) is the transmitted ray. The refracted (transimitted) ray (3) then interacts with the bottom interface and the reflected ray is (4) and the transmitted ray is (6). Lastly (4) interacts again with the top surface and some of it is transmitted (5). There are more reflections and transmissions, an infinite number in theory, but the first two are the most dominant due to the intensity decreasing at every interface. Now light rays (2) and (5) can interference with each other. They are coherent since they originated from the same source and there is a Path Length Difference (PLD) between the two. At near normal incidence the PLD is equal to twice the thickness tt of the film, PLD=2tPLD=2t. Now before using the standard integer multiple of the wavelength approach to constructive interference, you must first consider phase changes in the reflected rays.

When light reflects off a material with a higher index of refraction the reflected wave has a phase shift. The animation on the left shows a wave pulse on a string that displays the same feature. You can see the pulse coming in from the left is upward but reflects downward, shifting the wave a half of a cycle (ππ).

In contrast if light reflects off a material with a lower index of refraction, there is no ππ phase shift. Also notice that the transmitted waves never have any phase shift.

All of this means you have find the relative number of phase shifts between the first reflected wave (2) and the second reflected wave (5). An example would be the air => oil => water system described above. Oil has a higher index of refraction than oil, so ray (2) has a ππ phase shift. When ray (3) reflects off the bottom surface, it is in oil and bouncing off water. Since nwater<noilnwater<noil there is no phase shift in reflected ray (4) or in (5) since it is transmitted. Ray (2) and (5) are interfering but there is a relative phase shift between them. So you must switch the conditionals for constructive and destructive interference.

Here λfilmλfilm is the wavelength of the light in the film. You can use the index of refraction to determine λfilmλfilm

The most common place this effect is observed is on bubbles or oil slicks. The colors you see are because those are the wavelegths that match the conditions for more constructive interference. The colors change because there are different thicknesses in the film.

Now, take a look at the pre-lecture reading and videos below.