A camera lens (n=1.50) is coated with a thin film of...

A camera lens $(n=1.50)$ is coated with a thin film of magnesium fluoride $(n=1.38)$ of thickness $90.0 \mathrm{~nm}$. What wavelength in the visible spectrum is most strongly transmitted through the film?

Key Concepts

Optical Path Length

The optical path length is the product of the physical thickness of the film and its refractive index. It is a key factor in determining the phase difference between light waves reflecting from different interfaces, which in turn dictates whether interference will be constructive or destructive at a given wavelength.

Anti-reflection Coating (Quarter-Wave Coating)

An anti-reflection coating is designed to minimize reflection and maximize transmission at a specific wavelength, typically by using a film with an optical thickness equal to one-quarter of the target wavelength in the film. This causes destructive interference among reflected waves, significantly reducing glare and enhancing image quality in optical applications.

Thin Film Interference

Thin film interference is a phenomenon that occurs when light waves reflect off the multiple surfaces of a thin film, leading to interference effects. Depending on the optical path differences and phase changes acquired upon reflection, certain wavelengths can experience constructive or destructive interference, altering the intensity of the transmitted and reflected light.

Phase Change upon Reflection

When a light wave reflects at the interface between two media with different refractive indices, it can undergo a phase change. Specifically, a phase shift of ? (or 180 degrees) occurs when light reflects from a medium of lower refractive index to a medium of higher refractive index, an effect that must be accounted for when analyzing interference in thin films.

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