You are coating glass with a film of higher index of...

Name: Problem 42, Chapter 19: Physics: A Conceptual World View
Uploaded: 2020-06-24T13:06:41-08:00
Duration: 2 min 6 s
Channel: Sanjeev Kumar
Description: You are coating glass with a film of higher index of refraction. You make the thinnest film that will produce a strong reflection for a particular monochromatic light source. You then gradually increase the film's thickness until you find another strong reflection. How many times thicker is this film than the original?

You are coating glass with a film of higher index of refraction. You make the thinnest film that will produce a strong reflection for a particular monochromatic light source. You then gradually increase the film's thickness until you find another strong reflection. How many times thicker is this film than the original?

Key Concepts

Order of Interference

Interference in thin films can occur at multiple orders, where each order corresponds to an integer multiple in the equation governing constructive interference. The first strong reflection comes from the lowest order (m = 0), and subsequent strong reflections occur at higher orders (m = 1, 2, etc.). The film thickness increases as these orders increase, which is key to determining how much thicker a film must be to achieve the next instance of constructive interference.

Constructive Interference Condition

For constructive interference to occur in a thin film, the optical path difference together with any phase shifts must result in the reflected waves being in phase. Generally, this is expressed by an equation that relates the film thickness, wavelength, and any phase changes upon reflection, ensuring that the reflected waves reinforce each other.

Thin Film Interference

This concept refers to the interference of light reflected from the two surfaces of a thin film. The constructive or destructive interference that arises depends on the optical path difference between the waves reflected from the top and bottom surfaces of the film. It is a fundamental phenomenon in optics used to explain colors and enhanced reflections in coatings.

Phase Change on Reflection

When light reflects off an interface between two media with different refractive indices, a phase shift may occur. Typically, when light reflects from a medium with a higher refractive index than the one it is coming from, it undergoes a 180° (or ? radian) phase shift. This phase change is crucial in determining whether the interference between reflected waves is constructive or destructive.

Optical Path Difference

The optical path difference is the product of the physical thickness of the film and its refractive index, adjusted by any additional distance traveled due to internal reflections. This effective path difference determines the relative phase between the reflected beams, thus playing a key role in interference patterns.

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