# Thin film intereference

• AlexKappa
In summary, scientists are testing a transparent material with an index of refraction that varies with wavelength. A 310-nm-thick coating is placed on glass with an index of refraction of 1.50. The reflected light will have maximum constructive interference at two visible wavelengths, with one being at 358.6nm and the other at 191.4nm. The middle of the visible spectrum is approximately 550nm, and the film's index of refraction is approximately 1.3. The phase change at the thin film/glass interface and air/thin film interface can be ignored. The equation for constructive interference is 2nd = mλ_air.
AlexKappa

## Homework Statement

[/B]
Scientists are testing a transparent material whose index of refraction for visible light varies with wavelength as n = 30.0 nm^(1/2)/λ^(1/2), where λ is in nm.

A 310-nm-thick coating is placed on glass (n = 1.50) what visible wavelengths will the reflected light have maximum constructive interference?

## Homework Equations

λ_constructive = (2nd)/m where m = 1,2,3,4
Δφ = 2π*(2nd)/λ

d is thickness of film[/B]

## The Attempt at a Solution

[/B]
I am really confused by the index of refraction notation n = 30.0 nm^(1/2)/λ^(1/2), but what I got out was that in the visible spectrum, n < 1. So you have air where n = 1. the film where n < 1, and glass where n = 1.5 . So light will reflect off the film with no phase difference, and light reflects off the glass with a phase shift of π. So the light has to travel 2d and have a phase shift of mπ (m = 1,3,5...) to have constructive interference.

π = 2π*(2 * (sqrt(30nm)/(sqrt(λ))) * 310nm) / λ

using a calculator I got λ = 358.6nm

using 3π, I got λ = 191.4nm which isn't in the visible spectrum

This answer is sadly wrong because the online answer box says there are two wavelengths that will have constructive interference.

#### Attachments

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The middle of the visible is ## \lambda=550 \, nm ##. There ## n \approx \frac{30}{23.5} \approx 1.3 ## by this formula. ## \\ ## And an additional hint: The index ## n ## of the film does obey ## 1<n<1.5 ##. This means that a ## \pi ## phase change will occur upon reflection at both the thin film/glass interface and also at the air/thin film interface, so that it can be ignored. ## \\ ## And your equation is correct for constructive interference: ## 2nd=m \lambda_{air} ##.

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## 1. What is thin film interference?

Thin film interference is a phenomenon that occurs when light waves reflect off of a thin film, causing constructive and destructive interference. This results in the appearance of different colors or patterns depending on the thickness of the film and the wavelength of the light.

## 2. How does thin film interference occur?

Thin film interference occurs when light waves reflect off of the top and bottom surfaces of a thin film. Depending on the thickness of the film, the reflected waves may either reinforce or cancel each other out, resulting in a change in the color or intensity of the reflected light.

## 3. What is the difference between thin film interference and other types of interference?

Thin film interference is a type of interference that occurs specifically in thin films, such as soap bubbles, oil slicks, or anti-reflective coatings. Other types of interference, such as diffraction and interference from multiple slits, occur in different types of materials or structures.

## 4. What are some real-life applications of thin film interference?

Thin film interference is used in a variety of applications, including anti-reflective coatings on glasses and camera lenses, color-changing pigments in cosmetics and paint, and the production of holographic images. It is also an important phenomenon to consider in the design of optical devices, such as lenses and mirrors.

## 5. How does the color of thin film interference change with the angle of observation?

The color of thin film interference is dependent on the thickness of the film and the wavelength of the light, but it can also change with the angle of observation. As the angle of observation changes, the path length difference between the reflected waves also changes, resulting in a shift in the interference pattern and the perceived color. This can be seen in the iridescent colors of soap bubbles, which change as they are tilted in different directions.

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