Camera Lens A camera lens with index of refraction greater...

Camera Lens A camera lens with index of refraction greater than $1.30$ is coated with a thin transparent film of index of refraction $1.25$ to eliminate by interference the reflection of light at wavelength $\lambda$ that is incident perpendicularly on the lens. In terms of $\lambda$, what minimum film thickness is needed?

Key Concepts

Anti-Reflection Coating

An anti-reflection coating is a thin film applied to surfaces to reduce unwanted reflections by creating destructive interference between light waves reflected from different interfaces. The thickness and refractive index of the coating are chosen strategically so that the optical path difference leads to minimal net reflected light.

Destructive Interference Condition

Destructive interference occurs when the phase difference between two waves is an odd multiple of ? (or the optical path difference is an odd multiple of a half-wavelength). In thin films, after accounting for any phase changes upon reflection, the condition for destructive interference can be used to derive the specific film thickness necessary to cancel reflections.

Optical Path Difference

The optical path difference corresponds to the difference in phase accumulated by light traversing different paths, which is the product of the physical distance and the refractive index of the medium. In thin film interference, the optical path difference determines the conditions for constructive or destructive interference.

Phase Change on Reflection

When light reflects between media of different refractive indices, it can undergo a phase change. Specifically, a phase shift of half a wavelength occurs when light reflects from a medium of lower refractive index to one of higher refractive index. This concept is crucial in interference problems since it affects the net phase difference between interfering waves.

Thin Film Interference

Thin film interference is a phenomenon where light waves reflected from the top and bottom surfaces of a thin film interfere with each other. This interference can be constructive or destructive, depending on the phase difference between the two reflected waves. It is a key concept in understanding how coatings on optical devices minimize or enhance reflections.

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