Summarizing Thin Film Interference

Problem-Solving Strategies for Wave Optics

Step 1.Examine the situation to determine that interference is involved. Identify whether slits or thin film interference are considered in the problem.

Step 2.If slits are involved, note that diffraction gratings and double slits produce very similar interference patterns, but that gratings have narrower (sharper) maxima. Single slit patterns are characterized by a large central maximum and smaller maxima to the sides.

Step 3.If thin film interference is involved, take note of the path length difference between the two rays that interfere. Be certain to use the wavelength in the medium involved, since it differs from the wavelength in vacuum. Note also that there is an additional \(\lambda /2\) phase shift when light reflects from a medium with a greater index of refraction.

Step 4.Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is useful. Draw a diagram of the situation. Labeling the diagram is useful.

Step 5.Make a list of what is given or can be inferred from the problem as stated (identify the knowns).

Step 6.Solve the appropriate equation for the quantity to be determined (the unknown), and enter the knowns. Slits, gratings, and the Rayleigh limit involve equations.

Step 7.For thin film interference, you will have constructive interference for a total shift that is an integral number of wavelengths. You will have destructive interference for a total shift of a half-integral number of wavelengths. Always keep in mind that crest to crest is constructive whereas crest to trough is destructive.

Step 8.Check to see if the answer is reasonable: Does it make sense? Angles in interference patterns cannot be greater than \(\text{90º}\), for example.

Summary

• Thin film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change.
• When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a \(\text{180º}\) phase change (or a \(\lambda /2\) shift) occurs.

Glossary

thin film interference

interference between light reflected from different surfaces of a thin film