A transparent film (n=1.3) is deposited on a glass lens...

A transparent film $(n=1.3)$ is deposited on a glass lens $(n=1.5)$ to form a nonreflective coating. What is the minimum thickness that would minimize reflection of light with wavelength $500.0 \mathrm{~nm}$ in air?

Key Concepts

Thin Film Interference

Thin film interference is an optical phenomenon that occurs when light waves reflected at different interfaces of a thin layer interfere with each other. The interference can be constructive or destructive depending on the phase difference between the reflected waves. This concept is fundamental in optics for designing coatings that either enhance or minimize reflections.

Optical Path Length

The optical path length is the product of the physical thickness of a material and its refractive index. It represents the distance traveled by light in terms of the phase accumulated. In interference phenomena, matching the optical path length with a specific fraction of the wavelength is essential for achieving the desired interference condition.

Phase Change upon Reflection

When light is reflected at the boundary between materials of different refractive indices, a phase change can occur. Specifically, when light reflects from a medium of higher refractive index, it undergoes a phase shift of ? radians (half a wavelength). This phase shift must be taken into account when designing thin film coatings for interference, as it alters the relative phases of the reflected waves.

Quarter-wave Coating

A quarter-wave coating refers to a film whose optical thickness is one quarter of the wavelength of the incident light. This design ensures that the reflected waves from the top and bottom surfaces of the film are out of phase by 180 degrees, leading to destructive interference. This principle is used to minimize reflections on optical surfaces.

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