Thin-Film Interference and Anti-Reflection Coatings
Light reflected from the two faces of a thin film interferes, and whether the result is bright or dark depends on the film thickness and on a phase change at reflection. Lens coatings are that condition engineered on purpose.
What a learner can do afterwards
- Works out the condition for constructive interference in a film, including the reflection phase change
- Explains the colours of an oil film and of a soap bubble as it drains
- Designs the thickness of an anti-reflection coating for a stated wavelength
1 · Read
Light bounces off both faces of a thin film, and the two reflections interfere. A bounce off a higher index material flips the wave by half a cycle, while a bounce off a lower index one flips nothing. That half flip decides whether the round trip adds up or cancels.
A soap film in air flips at the front face only. Head on, bright films satisfy 2 n t equals m plus one half times the wavelength, and dark films satisfy 2 n t equals m times the wavelength. A very thin film goes dark at every colour, and as a bubble drains its thickness sweeps the bright condition across colours in turn.
A lens coating of magnesium fluoride sits on glass, and both reflections flip, so cancelling needs 2 t to equal half a wavelength inside the film. For 500 nm light and index 1.38 the thinnest layer is 500 divided by 4 times 1.38, which is 90.6 nm. Other colours are only partly cancelled.
To design a coating, pick the wavelength you most want to kill and make the layer a quarter of its wavelength inside the film. Quarter wave in, reflection out.
Track the two reflections and their flips, then choose the thickness so the target colour cancels.
2 · Watch
Take it off screen
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.