After watching this video, you will be able to explain how thin film interference works, give examples of thin film interference in everyday life and solve simple problems. A short quiz will follow.

## Thin Film Interference

When was the last time you played with bubbles? No, seriously, when? I recommend that you go out soon and do that… in the name of science! When you do, pay particular attention to the colors in the bubbles. If you’ve played with bubbles recently, or have a good memory, you might remember seeing little rainbows in the bubbles – a swirly mix of every color of the rainbow.

Or, if you’ve ever seen an oil slick floating on water, you might have noticed rainbows there, too. The most common time you might have seen that is if a car spilled oil near a puddle on a rainy day. The beautiful, reflective rainbow patterns definitely left a mark on 7-year-old me when I first saw them.

Both of these things are the result of a phenomenon called thin film interference. **Thin film interference** is where an interference pattern is created due to two or three different materials or layers sandwiched on top of each other. But let’s look at how it works in more detail.

## How Does It Work?

If you’ve already watched video lessons on diffraction, either single-slit or double-slit, the way thin film interference is created should be pretty familiar. When you shine light through a double-slit for example, the distance to the screen is different for each slit, and that leads to peaks or troughs arriving at different times. Those peaks and troughs interfere with each other, to produce a pattern of light and dark areas.Well, the same thing happens with thin film interference, just for a different reason.

The two or three layers (for example, oil, water and air) have different properties. When light goes through the boundary between two materials, it can either reflect off the boundary or refract (bend) through the boundary and into the next material. Because of this, the light that hits the sandwich of materials will refract at different points. Some will reflect off the outer surface, and some will reflect at a boundary between two materials. This creates a **path difference**, a difference in distance traveled by two beams of light. So, when the light reaches your eye, depending on the exact path difference, you’ll get some combination of peaks and troughs from each, leading to an interference pattern.If two peaks or two troughs combine together, you get a bright spot of a particular color, and this is called **constructive interference**.

If a peak and a trough combine together, they cancel each other out to give you a dark spot, and this is called **destructive interference**.But what about all the different colors? Why do you see a full rainbow? It turns out that light of different colors (of different wavelengths) refracts differently when it moves from one material to another. For it to refract and then reflect such that it ends up inside your eye, the thickness of the material has to be just right. If you have something like a bubble, where the thickness varies, you can get different colors at different points. That’s how you get your rainbow. But whenever you see a color, you’re seeing a maximum (a bright spot) in the interference pattern for that color.

## Equation

As we’ve discussed, the exact nature of the pattern depends on the color (or wavelength) of light and on the thickness of the material (and therefore the path difference), and since refraction occurs when you move from one material to another, it also depends on the indices of refraction of the materials involved.To make it even more complex, there is a phase change that sometimes occurs in a wave when it hits a mirror or reflective surface. When light reflects from a medium having a larger refractive index than the one in which it’s traveling, a 180-degree phase change occurs.

This is like a half wavelength shift in the wave. All those things must be taken into account when deriving an equation for thin film interference.When you put all that together, you get these equations for constructive and destructive thin-film interference.Destructive:2*n`film`*d*cos(theta`2`) = m*lambdaConstructive:2*n`film`*d*cos(theta`2`) = (m – 1/2)*lambdaHere, n`film` is the refractive index of the middle material – either the soap bubble or the oil – *d* is the thickness of the film measured in meters, theta`2` is the angle with which the light hits the film, lambda is the wavelength (or color) of the light and *m* is just a whole number, representing whether you’re looking at the first maxima, second maxima and so on. Sometimes the second and third maxima will be so dim you can’t even see them, so this number will often just be 1.These equations will work for a soap bubble with air on either side or an oil film with water underneath and air on top. This is because in both these cases, there is a phase shift for one wave and no phase shift for the other.

If the sandwiched materials were different and both waves had a phase shift or both waves didn’t have a phase shift, the equations would switch: the constructive interference equation would become the destructive and vice-versa.

## Calculation Example

In the finest physics tradition, it’s time to do an example problem! One day, you’re playing with bubbles, when you suddenly feel the urge to stare intently at one of them because they’re fascinating! You notice that the brightest band of a nice blue color (which just happens to be your favorite color) can be seen in a part of the bubble that has a different thickness to the rest. You use a laser imager to measure the thickness and find it’s 5 x 10-8 meters. The angle of the sun shining on the soap bubble is approximately 33 degrees, and after taking a photo of the bubble, you find that the wavelength of light that matches that color is 4.8 x 10-7 meters. Based on this information, what is the refractive index of the soap the bubble is made from?Okay, so the first step is to write out what we know.

We know that the thickness, *d*, of the bubble is 5 x 10-8 meters. We know that the angle of the light, theta, is 33 degrees; and we know that the wavelength of the light is 4.8 x 10-7 meters. We can also deduce that *m* is probably 1, since it’s the brightest band you can see. Now the only unknown left in the equation is the refractive index of the film, n`film`.We can do some algebra and rearrange the equation, to find out that the refractive index of the soap bubble is equal to 1 minus a half, multiplied by 4.8 x 10-7, divided by 2, also divided by cosine 33, also divided by 5 x 10-8 meters.

Type all of that into a calculator, and you get a refractive index of 2.86. And that’s it; we have our answer.

Constructive:(2)* n`film`*(5 x 10-8)*cos(33) = (1 – 1/2)*(4.8 x 10-7)n`film` = ((1 – 1/2)*(4.8 x 10-7)) / ((2)*(5 x 10-8)*(cos(33)))n`film` = 2.86

## Lesson Summary

**Thin film interference** is where an interference pattern is created due to two or three different materials or layers sandwiched on top of each other. This causes the colors you see on an oil slick or the rainbows you see in soap bubbles. These happen because the two or three layers (for example, oil, water and air) have different properties.When light goes through the boundary between two materials, it can either reflect off the boundary or refract (bend) through the boundary and into the next material.

Because of this, the light that hits the sandwich of materials will reflect at different points. Some will reflect off the outer surface, and some will reflect at a boundary between two materials. This creates a **path difference**, a difference in distance traveled by two beams of light.

So, when that light reaches your eye, depending on the exact path difference, you’ll get some combination of peaks and troughs from each, leading to an interference pattern. If two peaks or two troughs combine together, you get a bright spot, and this is called **constructive interference**. If a peak and a trough combine together, they cancel out to give you a dark spot, and this is called **destructive interference**. You see different colors, because different wavelengths of light refract (or bend) differently and so the bright spots for each color appear in different places.

The way the pattern looks depends on the color (wavelength) of light, on the thickness of the material (and therefore the path difference), on the indexes of refraction of the materials involved, and therefore whether a phase change occurs. Putting those factors together, you get these equations for constructive and destructive thin film interference:Destructive:2*n`film`*d*cos(theta`2`) = m*lambdaConstructive:2*n`film`*d*cos(theta`2`) = (m – 1/2)*lambdan`film` is the refractive index of the middle material – either the soap bubble or the oil – *d* is the thickness of the film measured in meters, theta`2` is the angle with which the light hits the film, lambda is the wavelength (or color) of the light and *m* is just a whole number, representing whether you’re looking at the first maxima, second maxima and so on. These equations assume that just one of the two waves has a phase change.

If both have a phase change, or neither do, the two equations switch places.To fully understand thin film interference requires knowledge of interference, waves and refractive indices (Snell’s law), and so it’s a topic that brings a lot of different parts of your physics knowledge together. But if we want to explain some of the most beautiful phenomena we see around us, we need to fully understand thin film interference.

## Learning Outcomes

Once you’ve completed this lesson, you should be able to:

- Explain what thin film interference is and why it occurs
- Recall what creates a path difference
- Differentiate between constructive and destructive interference
- Identify the equations for constructive and destructive thin film interference