# PhET Wave Interference Simulation

Play around with different types of waves to learn about interference and diffraction.

# Video Transcript

Hello there! Welcome to lecture 29: light waves!

Light has many fascinating properties and interacts in many meaningful and useful ways. By treating light as a wave and understanding its interference effects, we can learn about even more properties and applications of light in our lives.

Each of the following concepts will be discussed in this video: light models, Huygens’ principle, diffraction, thin-film interference, and polarization.

## Light models

So far, we have discussed how light travels by treating it like a ray. A beam of light travels from one place to another, and along the way it might bend (refract) or bounce (reflect). Possibly it might transmit or be absorbed. This simple model of light explains a lot: mirrors, lenses, rainbows, and other phenomena we’ve discussed in the past few lectures. This model of light is known as ray optics.

Ray optics is great in its simplicity, but there are aspects of light that cannot be explained by this model. We can expand our model to include the wave nature of light. This new model is known as wave optics. Treating light as a wave allows us to understand and quantify phenomena such as interference and diffraction: topics we’ll discuss in this lecture.

If we wish to expand our view of light even more, we can use the model of electromagnetic optics. This takes the wave nature of light into account, but also includes the fact that light is composed of electric-field and magnetic-field vectors oscillating in space. An electromagnetic approach to optics explains and quantifies phenomena such as light polarization.

Finally, a fully quantum model of light, quantum optics, can be used to explain all of the above phenomena, PLUS phenomena such as the photoelectric effect, lasers, semiconductors, and more. This is the most complicated and mathematically rigorous model of light, used to explain complex phenomena when the other models fall short. We will discuss some of these fascinating topics in lecture 31, but will not go into a full mathematical treatment of quantum optics.

## Huygens’ principle

Huygens’ principle states that every point on a wave can be treated as a spherical wave that itself propagates through time and space. Each of these individual spherical waves interact with each other through interference. Each individual spherical wave amplitude is added to the amplitude of every other individual spherical wave, and that sum total represents the total wave. Note that Huygens’ principle is a simplified model that we can use to understand some concepts, but it is not a complete theory of optics or electromagnetism.

For example, a plane wave is a light wave that travels through space with all of the wave crests and troughs aligned in straight lines. If we want to draw a plane wave, we can draw a line where the wave crests are, and note that they form parallel lines in space. A plane wave is a very simple type of wave to analyze mathematically, and is a nice approximation that physicists and engineers can use in optics calculations. Huygens’ principle says that we can represent each point on each wave crest in the plane wave as a spherical wave. The interference of those spherical waves causes what we see as a plane wave.

Huygens’ principle is particularly useful in describing what happens when light passes through a small opening. A plane wave traveling through a small opening will curve at the edges when it passes through. Because Huygens’ principle describes light as being a collection of spherical waves, it provides a description of that spherical shape at the edges.

The amount of curving relates to the wavelength of light traveling through as well as the size of the opening. The larger the width of the opening as compared to the wavelength of the wave, the less pronounced the curving of light will be. The smaller the width of the opening as compared to the wavelength of the wave, the more pronounced the curving of light will be.

## Diffraction

Diffraction is a bending of light as it travels around a corner or through a small opening. This happens with all light waves, but only creates a noticeable effect when the size of the opening is on the same size scale as the wavelength of the light.

The amount of bending that occurs in diffraction has to do with the wavelength of the light. The longer the wavelength, the more bending will occur, with all other things being equal.

Diffraction occurs not only with visible light, but all waves. This includes water waves in a ripple tank. We can see that the smaller the opening, the more spreading out occurs of the water waves. Diffraction also occurs with all types of electromagnetic waves, not just visible waves. Radio waves, for example, will diffract around buildings, mountains, and other terrain.

A diffraction grating is a component that has regularly spaced openings for light to pass through. By creating a periodic pattern, light will get diffracted through several different angles. This is because the spacing between the openings and the wavelength of light will cause regions of constructive and destructive interference. Where the interference is constructive, we will see bright spots. The destructive interference areas will be dark spots.

In this demo, I shoot a blue laser pointer through a diffraction grating that has 1000 lines per millimeter. On a screen 1 meter away, we can observe each of the bright spots indicating points of constructive interference. I used a ruler to measure the distance between each spot, which is 46 cm.

When I repeat this experiment using a green laser pointer the same distance away, and using the same diffraction grating, the spots are now spread farther apart: 65 cm. This is because the larger wavelength of green light as compared to blue light, given the same spacing on the diffraction grating, will cause the light to bend more.

Repeating the experiment with a red pointer gives the largest distance between spots: 90 cm. Red has the longest wavelength of visible light, and will therefore bend the most.

We can repeat the experiment one more time, keeping the red laser pointer, but using a different diffraction grating with only 500 lines per millimeter. Because the spacing is larger, the light will bend less. Indeed, it only spreads out 36 cm with this diffraction grating.

To sum up: the amount of bending that occurs with diffraction has to do with the wavelength of the light and the size of the spacing. The larger the wavelength is compared to the spacing, the more bending will occur.

It’s also possible to shine a white light source on a diffraction grating and see what happens. Because white light is composed of all other colors of light, we can observe each color getting split apart due to the different amounts of bending based on wavelength. When I shine a white light source on a diffraction grating, the longer wavelengths bend the most, and the shorter wavelengths bend the least. This results in a rainbow pattern.

Diffraction gratings have lots of uses in physics and engineering. When I was a graduate student, I would use a diffraction grating to determine how well different devices I designed in a clean room would emit different wavelengths of light. By focusing white light on the device, and taking the emitted light and sending it through a diffraction grating, each wavelength of light would be split apart. A recording device known as a CCD was used to measure the intensity of each wavelength. I could then use that recorded data to see what wavelengths of light my device emitted.

Scientists also use diffraction gratings to determine the composition of stars, including our sun. By looking at the different wavelengths of light that stars emit, and understanding the concept of light emission that we’ll discuss in lecture 30, scientists can determine what gases stars are made of.

You may have seen glasses that cause things to look like rainbows when you look through them at white light sources. These glasses are simply diffraction gratings!

One last thing about diffraction. Because light bends when it interacts with an opening, diffraction limits our ability to see really small things. This means that most imaging devices such as cameras and microscopes can only focus sizes that are larger than about one half of the wavelength of light that’s used. If the smallest wavelengths of visible light are 400 nm, that means the smallest things we can focus on using a microscope or camera will be larger than 200 nm. We cannot use visible light waves to see things smaller than that!

## Thin-film interference

When light waves reflect at the top and bottom interfaces of a thin layer of material, an interference pattern will be created. This phenomenon is known as thin-film interference.

If you’ve seen a rainbow in an oily water puddle, you’ve seen thin-film interference. In a thin puddle of oily water, a thin layer of oil will sit on top of the water. At just the right level of thickness, a single wavelength of light will experience constructive interference, leading to only a single color of light appearing on reflection. As the thickness of the oil changes at the end of the puddle, the changing thickness results in a rainbow.

Let’s see how the physics of this works. Say a thin film that’s equal to one quarter of the wavelength of light is layered on top of a reflective surface. When light of that specific wavelength (four times the thickness) hits that film, the wave will experience constructive interference. That means that one particular color will be reflected back with a larger intensity than other colors.

When a thin film is equal to one half of the wavelength of light, that specific wavelength will experience destructive interference. That particular color will not be reflected back at all.

Single thin films can be used to determine optical flatness. If I have a piece of glass, I can use thin-film interference with a single wavelength of light (known as monochromatic, as it only has one wavelength of light present). If the thickness of the piece of glass changes, this will result in areas of constructive and destructive interference.

I can demonstrate this with two pieces of glass and a sodium light source that is mostly monochromatic. As I press on the glass, changing the thickness of the air gap between the two pieces of glass, I can see many circular fringes, caused by constructive and destructive interference based on how thick the air gap is. If this was completely flat, the fringes would be straight lines.

You may also experience thin-film interference in other applications. By layering multiple thin films, it is possible to create an anti-reflection coating. These are used a lot on eyeglasses, cameras, microscopes, and other optical devices.

## Polarization

As mentioned, modeling light as a wave allows us to understand properties of light such as interference and diffraction. Expanding our model to encompass electromagnetism allows us to understand the property of polarization. Recall that light is composed of electric fields and magnetic fields oscillating at right angles to each other. Light is a transverse wave, which means the motion of the light is at right angles to both the electric and magnetic fields.

Polarization is the property of transverse waves which allows them to have their electric field components oriented in a single direction. Essentially, the electric fields oriented in any other direction can be blocked by a polarizing filter, allowing only a single orientation of waves to travel through space.

Most light sources generate light waves with all orientations of electric fields, known as non-polarized light. This light can be passed through a polarizing filter, which only allows light of a certain orientation to pass through. The light is now polarized. If we think of non-polarized light as the sum of all polarizations of light, we can consider that 50% of that light will have horizontal electric fields, and 50% of that light will have vertical electric fields. By placing a single polarizer at a horizontal angle, I’ve now blocked all of the horizontally polarized light from passing through. Placing a second polarizer at a 90-degree angle to this one now blocks all of the vertically polarized light from passing through. Placing two filters at 90-degree angles will block all light from passing through.

Now if I place a third polarizer in the center at a random orientation, light is able to pass through again. Why is this? We can think of the vector orientation of the light as it passes through each filter. The first causes the light to be oriented vertically. The second light takes only the components of that vertical light that is oriented at its particular angle and allows it through. Finally, the horizontal polarizer takes the component of that angled light that’s horizontal and allows it through. To completely block light, two adjacent polarizing filters must be at 90 degree angles to each other.

Perhaps you own polarized sunglasses. Light that reflects off of a surface at a very steep angle, at an angle greater than something known as Brewster’s angle, will have only one polarization of light. The other polarization of light does not reflect. This means that any polarizing filter that blocks that reflected light will eliminate glare from steeply angled reflections. This is what polarized sunglasses do!

When wearing polarized sunglasses, it can be very obvious when you look at something that generates polarized light, such as LCD screens. By tilting your head 90 degrees while wearing polarized sunglasses, you can see polarization effects. Not only do LCD screens and monitors have polarization effects, but so do heat treated windshields in cars.

One last thing about polarization. Some objects have an index of refraction that changes based on the polarization of light. This means that light in one polarization will bend more than light at the cross polarization. These objects are known as birefringent. A birefringent crystal placed over words shows this property by creating a double image: one of the images is polarized in one orientation, and the other image is polarized in the opposite orientation. I can take a polarizing filter and rotate it and see how one image is blocked, then the other, depending on the orientation of the filter.

Thanks for taking the time to learn about light waves! Until next time, stay well.