Short on time? This page is the recap. For explanations, Figure 1 and the worked examples, use the full study guide.
Recap
- At a boundary, light is partly reflected, partly transmitted and partly absorbed.
- A thin film reflects from its top and bottom surfaces. The two reflected waves overlap and interfere.
- The effect shows when the thickness is comparable to the wavelength (hundreds of nm).
- Interference depends on film thickness, wavelength, reflection phase changes and viewing angle. Calculations use normal incidence only.
- Soap and oil films show colour bands because their thickness varies. A film much thinner than λ with one phase change looks black.
- An antireflection coating makes the two reflections cancel, so more light is transmitted.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| reflection from higher n → 180°; from lower n → 0° | phase change on reflection | count phase changes (0, 1 or 2) |
| λ_film = λ / n_film | wavelength inside the film; f unchanged | compare the path with the right wavelength |
| extra path = 2t | normal incidence, down and back | find the path difference |
| 0 or 2 changes: bright 2n t = mλ, dark 2n t = (m + ½)λ | m = 0, 1, 2, … | predict reflection colours |
| 1 change: bright 2n t = (m + ½)λ, dark 2n t = mλ | conditions swap | predict reflection colours |
| t_min = λ / (4n_coating) | quarter-wave antireflection coating, n_air < n_coating < n_lens | design a coating |
Assumptions behind the numbers
- Light hits the film at normal incidence.
- λ without a label is the wavelength in air (n = 1.00).
- Visible light runs from about 400 nm to 700 nm.
- Absorption in the film is small enough to ignore in the interference conditions.
Mistakes to avoid
- Flipping every reflection. Only reflection from a higher n gives 180°.
- Adding a phase change for refraction. Refraction never changes the phase.
- Using t instead of 2t.
- Using λ in air inside the film. Divide by n_film, or write 2n t.
- Using one formula for all films. One phase change swaps bright and dark.
- Choosing a coating index above the lens index. That gives one phase change and makes reflection stronger.
Quick self-check
- What is the wavelength of 520 nm light inside a film with n = 1.30? (400 nm)
- Light in glass reflects from the glass–air surface. Is there a phase change? (No: air has the lower n)
- Minimum thickness of a coating (n = 1.25) on glass (n = 1.52) that cancels 600 nm reflection? (120 nm)
- Why does a soap film look black just before it bursts? (t ≪ λ and one phase change, so the reflections cancel for every colour)
Next: practice questions.