# PHYS 2212 Module 15.1

## Young’s Double-Slit Interference

15.1 Young’s Double-Slit Interference

### Learning Objectives

By the end of this section, you will be able to:

• Explain the phenomenon of interference
• Define constructive and destructive interference for a double slit

### Wave Interference

To make sense of how wave optics work, it is necessary to understand wave interference first. You learned about waves in PHYS 2211 and discussed wave interference, most likely for sound waves. But all waves can interfere – it is a property of waves only. Watch this video to remind you of wave interference. Professor Dave uses sound waves in his discussion, but it can apply to light waves, too, which is what we will discuss in this module.

### Constructive and Destructive Interference

In the animation below, the wave on the bottom is the superposition of the two waves on top, the resultant when the two top waves add together. You can see how the amplitude of the resultant wave gets bigger and smaller depending on how the two waves on top are aligned or not aligned with each other. When the two waves are in phase, they constructively interfere and the resultant wave’s amplitude is a maximum. When the two waves are out of phase, they destructively interfere and the resultant wave’s amplitude is a minimum (zero).

If these waves were light waves and they were directed at a screen, then when the waves were in phase (constructive interference) you would see a brightly-lit spot on the screen. And when the waves were out of phase (destructive interference), you would see no light projected on the screen.

### Wavefronts

If you look at a still body of water, like a pond or a puddle, when it begins to rain, you can see circular waves form and spread out from the point where a raindrop falls, like in this picture:

Those circular waves you see, where the amplitude is a maximum, are called wave fronts. They travel outward from the source of the wave (the raindrop) radially at the speed of the wave. Here it would be the speed of a wave in water. If this was light, then the wavefronts would travel at the speed of light, c.

Now pretend you are standing at the edge of a pond, but it’s not raining anymore. You can create circular wavefronts by tapping the surface of the pond repeatedly with your fingertip. If you did this with two fingers you would produce two waves that would propagate outward from each of your fingers. These waves would interfere with each other, in some places constructively and other places destructively. Here is what that might look like:

So wavefronts can interfere with each other constructively and destructively. Another thing wave fronts can do is bend around corners. If you put an obstacle in the way of a wave, it will spread out around the obstacle, like you can see in this picture:

In this picture, the light waves are coming from the left and they encounter an obstacle (the ball). Notice how the incident waves are plane waves, meaning that the wavefronts are straight lines. But when the wave bends around the ball, the wave fronts spread out and become circular. Then they spread out even more and interfere with each other. This is called diffraction and it is based on Huygen’s Principle.

### Huygen’s Principle

Every point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wavefront is a line tangent to all of the wavelets.

In this animation, plane waves are coming from the left and encounter a yellow screen with a small opening (called a slit). You can see the little sources (little dots) that produce circular wavelets as the wave travels through the slit. These wavelets combine to produce circular wavefronts as the wave passes through the slit, and these wavefronts spread out. If this was light and we put a screen on the right side of this picture, then you would see a diffraction pattern on the screen – a series of bright spots and darks spots, like this:

The bright spots are due to constructive interference of the wavelets and the dark spots are due to destructive interference. The rest of this module will be about this concept. It turns out we can deduce many things about the light and the obstacle (the slit or multiple slits) by analyzing a diffraction pattern like this. It is the basis of a technique called X-ray Crystallography, which is used to determine the structure of atoms/molecules in a crystal. It was the technique used to determine that DNA has a double-helix structure. Here is the diffraction pattern that Rosalind Franklin produced with X-ray Crystallography:

Another really interesting phenomenon that occurs because of diffraction and the interference of light waves is called thin film interference. We will discuss this at the end of the module. But to give you a preview, thin film interference explains why soap bubbles have that swirly, iridescent pattern:

and why the Blue Morpho Butterfly’s wings are this color:

### Young’s Double Slit Experiment

Before we get into the nitty gritty of the double slit experiment, watch this video from (one of my favorite You Tube channels) Veritasium: