SPH 4UI

Wave Theory of Light

Lesson 5 – Thin Film Interference
With the work of Thomas Young providing evidence that light is a wave, we are now able to investigate different types of interference. One interesting phenomenon is the appearance of colours, visible on soap bubbles and thin films of oil and gasoline. The thickness of these thin films and the refractive index of the materials play an important role in the interference occurring.

With thin films, some of the light falling onto the top surface of the transparent film is reflected. Some light, unreflected, travels through the film until it meets the lower surface where, again, some light is reflected.
This light reflected from the bottom surface travels back through the medium and rejoins the reflected light from the top surface.
Path Difference Effect
The path difference between the reflected light and the light that travels down and back through the film is what determines the relative phase shift between the two waves. Due to its journey within the film and its reflection from the bottom surface, this light wave may have a different phase to the light reflected from the upper surface.
Recall the conditions for interference:
Constructive

Destructive

We also need to correct for the changing wavelength of light as it moves through the film, which has a different refractive index.

SPH 4UI

Wave Theory of Light

The Reflection Effect
Recall that when a wave reflects off of a dense barrier, it changes its phase.
In grade 11 physics, we investigated this effect with springs and applied its use to sound.

Combining the Effects
When the two waves, now phase shifted with respect to each other recombine, interference happens. If they interfere constructively, a bright colour appears. If they interfere destructively, no colour appears.
In general, there is no one formula to define this behaviour. To solve these types of problems we follow a specific process. Here is an outline of some simple steps to follow.
1. Determine the number of wavelengths the incident ray travels inside the film.
Remember that since the velocity of light changes in the new medium and the frequency does not, the wavelength must change. Find the new wavelength λ using n2 = 1 . λ2 2. If the