A soap film has an index of refraction n=1.50. The film is...

A soap film has an index of refraction $n=1.50$. The film is viewed in reflected light. (a) At a spot where the film thickness is $910.0 \mathrm{~nm}$, which wavelengths are missing in the reflected light? (b) Which wavelengths are strongest in reflected light?

Key Concepts

Thin?Film Interference

Thin?film interference occurs when light reflects off the two boundaries of a thin film, producing two (or more) coherent waves that overlap and interfere. The resulting pattern of bright and dark fringes depends on the optical path difference between the waves, which is influenced by the film’s thickness, the light’s wavelength, and the refractive index of the film.

Phase Change upon Reflection

When light reflects from a surface, it can undergo a phase shift depending on the relative refractive indices of the media involved. In particular, reflection from a medium of higher refractive index introduces a ? (half-wavelength) phase shift, and this modification is crucial in predicting the interference effects in thin films.

Optical Path Difference

The optical path difference between the two reflected waves is a product of the film’s refractive index and its thickness, typically expressed as 2nt for a film of thickness t. This extra distance traveled by one of the beams, combined with any phase shifts on reflection, determines the relative phase of the waves when they recombine.

Interference Conditions (Constructive and Destructive)

Constructive interference (resulting in enhanced or strongest reflected light) occurs when the phase difference between the waves is an integer multiple of 2?, while destructive interference (leading to missing wavelengths) occurs when the phase difference results in cancellation of the wave amplitudes. In thin film problems these conditions are defined by equations that involve the wavelength, film thickness, and refractive index, along with any phase changes upon reflection.

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