A beam of monochromatic light experiences constructive...

A beam of monochromatic light experiences constructive interference when it shines on a soap film with a thickness of $183 \mathrm{~nm}$ and an index of refraction of $1.35$. What is the wavelength of the light?
(Assume that $m=0$.)

Key Concepts

Interference Conditions

Interference conditions determine when waves will add constructively or destructively. For constructive interference in thin films, the total phase difference, which includes contributions from the optical path difference and any phase shifts upon reflection, must be an integer multiple of 2?. This condition is essential for tasks such as determining the wavelength that results in constructive interference in a given film.

Phase Shift upon Reflection

When light reflects off a boundary leading to a medium with a higher refractive index, it undergoes a phase shift of ? radians (equivalent to a half-wavelength). This phase change must be taken into account when determining the interference condition, as it effectively alters the required optical path difference for constructive or destructive interference.

Thin Film Interference

Thin film interference occurs when light waves reflect off the two boundaries of a thin film, and the resulting waves overlap. The constructive or destructive interference produced depends on the differences in the optical paths taken by the light through the film, which is influenced by the film’s thickness and refractive index, as well as any phase changes incurred during reflection.

Optical Path Difference

The optical path difference is the product of the physical path length and the refractive index of the medium. It quantifies the effective distance traveled by light in a medium relative to propagation in vacuum, and is crucial in calculating the phase difference between waves reflecting from different interfaces in the film.

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