The reason soap bubbles and oil films on water appear rainbow-colored is thin-film interference. The key is to handle the phase change upon reflection (a half-wavelength shift) accurately.
Basic Knowledge
Thin-film interference: When light enters a thin film of thickness t (refractive index n₂, with surrounding media n₁ and n₃), the reflected light from the top and bottom surfaces interferes.
Optical path difference: 2n₂t（the distance for a round trip inside the thin film）
Phase reversal (half-wavelength shift): Reflection at a boundary from a low refractive index to a high refractive index causes a phase change of π (a half-wavelength shift). Reflection from high to low causes no change.
Example: In the case of a thin film (n=1.5) on air (n=1) (phase reversal upon reflection from the top surface and no change upon reflection from the bottom surface):
・Constructive interference（bright）: 2n₂t = (m + 1/2)λ（m = 0, 1, 2, …）
・Destructive interference（dark）: 2n₂t = mλ
（When there is one phase reversal. The conditions differ when there are two or zero phase reversals）
Thin-film interference（The phenomenon in which reflected light from the top and bottom surfaces of a thin film interferes）
Optical path difference（The difference in refractive index × path length. 2n₂t is the optical path difference in thin-film interference）
Phase reversal（A half-wavelength shift produced by reflection from a medium with low n to one with high n）
Newton’s rings（Concentric interference fringes produced by a thin air layer between a plano-convex lens and a flat glass plate）
Anti-reflection coating (AR coating)（A coating that uses thin-film interference to weaken reflection and increase transmission）
Further Study (Background・Significance)
Soap bubbles appear rainbow-colored because the thickness of the film varies from place to place, causing different wavelengths (colors) to be emphasized at different locations according to the interference conditions. Just before a soap bubble disappears, the film becomes extremely thin and the entire bubble becomes black (destructive interference).
Anti-reflection coatings are designed with a film thickness such that 2n₂t = λ/2 (optical path difference = λ/2, producing destructive interference when phase reversal is considered). The blue-violet color of camera lenses results because red and blue light at the edges is reflected when the coating is optimized for green light at the center of the visible spectrum.
The wavelength can be measured precisely from the radius of the m-th bright ring in Newton’s rings, rm = √((m+1/2)λR)（R: radius of curvature of the lens）.
- Optical path difference in thin-film interference = 2n₂t
- Phase reversal (half-wavelength shift) upon reflection from low to high refractive index
- Bright and dark conditions change according to the number of phase reversals (0・1・2)
- Anti-reflection coating: uses destructive interference from thin-film interference
- The rainbow colors of soap bubbles and oil films are caused by thin-film interference
Points to Note (Easily Confused)
① Phase reversal occurs only upon reflection from “low to high refractive index.” There is no phase change for reflection from “high to low.” Check the refractive indices at the boundaries for each problem. ② In the optical path difference 2n₂t, n₂ is the refractive index of the thin film (not the surrounding medium). ③ With one phase reversal, the conditions for constructive and destructive interference are reversed from those for ordinary interference. ④ The center of Newton’s rings (air-layer thickness = 0) is a dark spot because there is one phase reversal.
Practice
- For normal incidence on a thin film in air (n = 1.4, thickness t), express the minimum film thickness for constructive interference of reflected light using the wavelength λ.
- Explain why a soap bubble becomes black just before it disappears from the viewpoints of phase reversal and optical path difference.
- Explain how an anti-reflection coating works using the terms “thin-film interference” and “phase reversal.”