# Diffraction of Light Waves

Hi, and welcome to this video on the diffraction of light waves! In this video, we will compare and contrast diffraction and dispersion and take a look at how diffraction gratings work. Let’s get started!

Dispersion and diffraction are each descriptions of light interacting with matter in different ways, and both can be used to separate light of multiple wavelengths. Let’s take a look at each of them separately.

Dispersion occurs when light of different wavelengths, such as white light, hits a refracting surface, like a prism. When white light hits the refracting surface, the different colors of light separate because of their differing wavelengths. Shorter wavelengths (violet) get refracted more than the longer wavelengths (red). They refract again once they leave the prism due to the differences in refractive properties between air and the prism.

Refractive materials are described by their optical density, which is a measure of how much of the light gets absorbed by atoms in the material. The higher the optical density of a material, the slower light is able to pass through it. While light travels at about $$3 x 10^{8} m/s$$ in a vacuum, it travels slower through any medium, depending on the optical density. The term used to measure the ratio of the speed of light in a vacuum, c, to the speed of light in a medium, v, is called the index of refraction: n=c/v, and it is also an indication of the optical density of a material.

The more optically dense a material is, the higher the index of refraction.

The amount of light absorbed by the refractive material depends on the wavelength of the light. In other words, materials have a range of optical densities corresponding to different wavelengths.

So, the whole picture of dispersion is that the different wavelengths of light are absorbed differently by the atoms in the refractive medium, which results in slightly different indices of refraction and slightly different angles of refraction for each wavelength of light, thereby dispersing the light.

Diffraction, on the other hand, refers to the phenomenon of waves bending as they pass through an opening or around the edge of an object.

The amount that the wave bends depends on the size of the wavelength and the size of the opening, or aperture. If these two things are similar in size, then the light can be bent more. Since the wavelengths of visible light are very, very small, this phenomenon may not be very intuitive.

Let’s look at water waves. If you’ve ever been to the ocean, you can imagine the waves of water rolling in. But, what happens when there’s a wall placed in the water with a small opening? Let’s take a look.

Since the water waves are similar in size to the opening in the wall, the bending of the waves is visible here. It works the same way with light!

When we shine a beam of light through a tiny aperture onto a wall or screen, we see a diffraction pattern. This pattern appears as a series of bright spots.

This experiment is referred to as the single slit experiment. It creates a pattern with the brightest spot in the middle, which fades to a dark spot, then a light spot again that is slightly less bright on either side until the bright spot fades completely. The dark spots are known as minima.

The equation used to describe this pattern based on each individual dark spot is, sine of theta equals n times lambda over d.
$$sin\Theta =\frac{n\lambda}{d}$$

θ is the angle from the center of the screen to the minima being measured, λ is the wavelength of the light, d is the size of the aperture, and n is the number of minima you are away from the center (1,2,3…). From this equation, we can see that as we decrease the size of the aperture d, the angle at which the light diverges increases, meaning that it will be bent more with smaller aperture openings.

The bright spots in the pattern, which we call “maxima”, are created through constructive interference, where the light waves meet up crest to crest or trough to trough and are combined, increasing the amplitude. The minima are created by destructive interference, where the light waves meet up out of phase, or crest to trough, and cancel each other out.

In a single slit experiment, the light pattern is not resolved very well, meaning that it gets brighter and darker gradually. However, we can get better resolution if we increase the number of openings to two or more.

Now let’s talk about diffraction gratings. Diffraction gratings are little slides with several, equally spaced slits of a given size, usually very small. When a light beam is passed through the grating, there are many more opportunities for constructive and destructive interference to occur, since the light is bending around multiple openings, compared to the single slit. This is why we get much sharper patterns with these types of gratings.

Multiple slit diffraction is described by the equation, sine of theta equals m times lambda over d.
$$sin\Theta =\frac{m\lambda}{d}$$

θ is the angle from the center of the screen to the maxima being measured, λ is the wavelength of the light, d is distance between slits, and m is the number of maxima you are away from the center. So, this equation is slightly different than that of a single slit because we are measuring to the maxima instead of the minima.

Since diffraction gratings can resolve light based on the wavelength and aperture size, we can also use these gratings to resolve white light into its different colors, like a prism would. Although, with diffraction, the process is not based on the index of refraction.

Now that we’ve discussed dispersion and diffraction and how they are alike and different, let’s check our knowledge with a couple of questions!

1. If you have two different refractive objects and you know that light travels faster through one than the other, which one has a higher index of refraction? Which one is more optically dense?

1. The one that light travels faster through has a higher index of refraction, but the other is more optically dense.
2. The one that light travels slower through has a higher index of refraction, but the other is more optically dense.
3. The one that light travels faster through has a higher index of refraction and is more optically dense.
4. The one that light travels slower through has a higher index of refraction and is more optically dense.

The correct answer is D. If light travels slower through a material, it is more optically dense, by definition. The index of refraction is the ratio c/v, so when the velocity, v, in a medium is lower, the index of refraction is higher.

2. True or False: A radio wave with a wavelength of 1 meter passing through a doorway will create a diffraction pattern.

The correct answer is True! All types of waves have the ability to be diffracted. Since the doorway is similar in size to the wavelength of a radio wave, it would be diffracted and create a diffraction pattern. However, radio waves are not visible. If radio wave detectors were set up along the wall, the pattern could be detected.

That’s all for this review! Thanks for watching, and happy studying!