The walls of a soap bubble have about the same index of...

The walls of a soap bubble have about the same index of refraction as that of plain water, $n$ = 1.33. There is air both inside and outside the bubble. (a) What wavelength (in air) of visible light is most strongly reflected from a point on a soap bubble where its wall is 290 nm thick? To what color does this correspond (see Fig. 32.4 and Table 32.1)? (b) Repeat part (a) for a wall thickness of 340 nm.

Key Concepts

Thin Film Interference

Thin film interference is a phenomenon where light waves reflected from the top and bottom surfaces of a thin film combine to produce a pattern of constructive or destructive interference. This interference depends on the optical path difference, which is a function of the film's thickness, its index of refraction, and the wavelength of light. This is the underlying principle used to explain the vibrant colors seen in soap bubbles and oil slicks.

Phase Change upon Reflection

When a light wave reflects off a boundary between two media, it may undergo a phase change. Specifically, if the reflection happens from a medium of lower refractive index to a medium of higher refractive index, a half-wavelength (or ? radian) phase shift occurs. Conversely, if light reflects from a higher to a lower index medium, no phase shift occurs. This phase change is crucial for accurately predicting the conditions for constructive interference in thin films.

Optical Path Difference

The optical path difference is the extra distance that light travels in the film relative to the light that reflects from the first surface. It is calculated as twice the product of the film's physical thickness and its refractive index. This value, when compared to the wavelength of the incident light (with adjustments for phase shifts due to reflection), determines the specific wavelengths that undergo constructive interference and thus are most strongly reflected.

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