# How Does Thin Film Interference Affect Light Reflection?

• DottZakapa
In summary, the problem involves a light wave with a wavelength of 648 nm and an incident angle of 90 degrees on a film with a thickness of 8.76 micrometers and a refractive index of 1.35. Part of the light is reflected from the first surface of the film while the rest enters the film and is reflected back at the second surface. The question asks how many wavelengths are contained in this round trip and what the phase difference is between the two reflected parts of the light. The answer is that there are approximately 36.5 wavelengths and the phase difference is 0, resulting in constructive interference.
DottZakapa
Homework Statement
Light with wave length 648 nm in air is incident perpendicularly from air on a film 8.76 micrometers think and with refractive index 1.35. par of the light is reflected from the first surface of the film, and part enters the film and is reflected back at the second surface where the fil is again in contact with air. How many waves are contained in its round trip through the film? What is the phase difference between these two parts of the light as they leave the film?
Relevant Equations
thin film
Homework Statement: Light with wave length 648 nm in air is incident perpendicularly from air on a film 8.76 micrometers think and with refractive index 1.35. par of the light is reflected from the first surface of the film, and part enters the film and is reflected back at the second surface where the fil is again in contact with air. How many waves are contained in its round trip through the film? What is the phase difference between these two parts of the light as they leave the film?
Homework Equations: thin film

the light incident on the film, having an index of refraction lower than the film has a phase difference of ##\frac{λ}{ 2}## the reflection from the second surface has no phase difference, therefore the formula for thin films in order to see a reflection would be

##2t=\frac{λ}{ 2}##

i don't understand how to answer the question... can anyone give some help?

These problems are most easily done by introducing the optical path length which is ## OPL= 2nt =2(1.35)(8.76 \cdot 10^3 ) ## nm, rather than converting the wavelength in air to its wavelength in the material. Meanwhile ## \lambda =648 ## nm. The question should read "how many wavelengths..." and not how many waves. That calculation is of course quite simple, and is ## x=\frac{OPL}{\lambda} ##. ## \\ ## For the next part, the phase change from the reflection off the front surface is ## \pi ##, (which does correspond to half of a wavelength), but the correct way of saying the phase change is to call it ## \pi ## (radians).## \\ ## For the second question, they could be more descriptive, because the problem involves the interference of coherent light waves. Whatever result you get for ## x ##, you subtract off any integer, and just take any remaining fraction and multiply by ## 2 \pi ##. I did the arithmetic and this one turns out to be almost a round number. I'm going to bend the rules here, because I really can't explain the concepts properly without pretty much giving the answer at the same time. The arithmetic I did gave me ## x=36.5 ##. That is the answer to the first part of the problem, but when you answer the question about phase difference, the 36 gets dropped, (it accounts for a total phase of ## (36)(2 \pi) ##, but integers of ## 2 \pi ## have no effect on the interference). This leaves ## \phi_{back \, surface}= (.5)(2 \pi) =\pi ##, while ## \phi_{front \, surface}= \pi ##, so that there is a phase difference of ## \phi=0 ## between the two reflected waves, and thereby constructive interference. IMO, this problem is good for an example problem, but it is asking a lot of the students in an introductory class to solve it on their own.

DottZakapa

## What is thin film reflection of light?

Thin film reflection of light is a phenomenon where light waves are reflected off of a thin layer of material, such as a soap bubble or a film of oil on water. This reflection occurs due to the difference in refractive index between the two sides of the thin film.

## How does thin film reflection of light work?

When light waves hit a thin film, some of the light is reflected off the top surface while some of it enters the film and is reflected off the bottom surface. These two reflected waves interfere with each other, creating a pattern of light and dark areas. The colors seen in thin film reflection are a result of this interference pattern.

## What factors affect thin film reflection of light?

The thickness of the film, the angle at which light enters the film, and the difference in refractive index between the film and the surrounding medium all play a role in thin film reflection. Additionally, the type of material used for the film can also impact the colors observed.

## What are some applications of thin film reflection of light?

Thin film reflection is used in a variety of applications, including in anti-reflective coatings for glasses and camera lenses, in optical filters, and in decorative items such as iridescent jewelry and bubble art.

## How is thin film reflection different from other types of reflection?

Thin film reflection is different from regular reflection because it involves multiple reflections and interference, rather than just one reflection off of a smooth surface. This results in the unique colors and patterns observed in thin film reflection.

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