Thin-film interference explains the bright shifting colors seen in soap bubbles, oil slicks, and anti-reflection coatings. It happens when light reflects from the top and bottom surfaces of a very thin transparent layer. The two reflected waves overlap, and their peaks and troughs can reinforce or cancel each other.
This makes some wavelengths appear bright while others disappear, so white light separates into visible colors.
Key Facts
- For near-normal incidence in a film, the extra path traveled inside the film is approximately 2nt, where n is the film refractive index and t is its thickness.
- A reflection from a boundary with higher refractive index causes a phase shift of λ/2, equal to 180 degrees.
- A reflection from a boundary with lower refractive index causes no phase shift.
- If exactly one reflected ray has a λ/2 phase shift, constructive reflection occurs when 2nt = (m + 1/2)λ.
- If exactly one reflected ray has a λ/2 phase shift, destructive reflection occurs when 2nt = mλ.
- For non-normal viewing, the path difference depends on angle, so the observed color changes as the film or viewer moves.
Vocabulary
- Thin film
- A thin film is a transparent layer with thickness comparable to the wavelength of visible light.
- Interference
- Interference is the combining of waves so that they reinforce or cancel based on their relative phase.
- Phase shift
- A phase shift is a change in the timing of a wave, often measured as a fraction of a wavelength or in degrees.
- Optical path length
- Optical path length is the physical distance light travels multiplied by the refractive index of the material.
- Constructive interference
- Constructive interference occurs when waves meet mostly crest to crest, producing a larger amplitude.
Common Mistakes to Avoid
- Ignoring the reflection phase shift is wrong because one reflected ray may flip by λ/2 while the other does not, changing bright conditions into dark conditions.
- Using 2t instead of 2nt is wrong because wavelength and phase inside the film depend on the refractive index of the film.
- Assuming all wavelengths are bright at the same thickness is wrong because each color has a different wavelength and satisfies the interference conditions at different film thicknesses.
- Applying the normal-incidence formula at large angles without adjustment is wrong because oblique rays travel a longer path through the film and change the interference condition.
Practice Questions
- 1 A soap film has refractive index n = 1.33 and thickness t = 120 nm. For reflected light at near-normal incidence with one λ/2 reflection phase shift, what wavelength has first-order constructive interference using 2nt = (m + 1/2)λ with m = 0?
- 2 An anti-reflection coating has refractive index n = 1.38 and is designed to destructively reflect green light of wavelength 552 nm in air. If one reflected ray has a λ/2 phase shift, use 2nt = mλ with m = 1 to find the minimum coating thickness.
- 3 A soap bubble changes from blue to yellow as it thins and shifts in shape. Explain how changes in film thickness and viewing angle can change which wavelengths interfere constructively in reflected light.