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

A camera lens $(n=1.50)$ is coated with a thin layer of magnesium fluoride $(n=1.38) .$ The purpose of the coating is to allow all the light to be transmitted by canceling out reflected light. What is the minimum thickness of the coating necessary to cancel out reflected visible light of wavelength $550 \mathrm{nm} ?$

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Key Concepts

Thin Film Interference

This phenomenon occurs when light waves reflect from the boundaries of a thin film and interfere with one another. The interference can be constructive or destructive depending on the optical path difference and any phase shifts that occur upon reflection. This principle is essential in designing coatings that either enhance or cancel out reflections.

Anti-reflective Coating

An anti-reflective coating is a thin layer applied on optical surfaces to reduce the reflection of light. By carefully choosing the thickness and refractive index of the coating, the reflections from the top and bottom surfaces of the film can be made to interfere destructively, thereby minimizing the overall reflected light and maximizing the transmitted light.

Optical Path Length and Phase Change

The optical path length is the product of the physical thickness of the film and its refractive index, which determines the phase shift that an incident wave experiences as it traverses the film. Additionally, when light reflects off a medium with a higher refractive index, it undergoes a phase shift of ? radians (180°). This combination of optical path difference and phase change is used to calculate the precise coating thickness required to achieve destructive interference for a particular wavelength.

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