# Workout: Interference from two wide slits

## Read

Two-slit interference, Diffraction, and Interference from two wide slits

## Launch

Download the simulation, Multiple Slit Diffraction, from the Open Source Physics website. You may need to update your java and tell your computer that this file is OK to run it.

(This is a nice simulation because it also shows what the pattern looks like, but if you cannot get it to run, answer the questions using the Desmos graphing calculator and the simplified equation (4) from Interference from two wide slits.)

## Set up

This sim allows you to see what the pattern would actually look like on a dark screen from the diffraction and interference of 1 to 20 slits of varying separations and widths.

When it comes up it shows a description window that describes what is being plotted and a simulation window. In the simulation window it should a two-slit pattern for light of 400 nm (0.40 μm) wavelength hitting two 10 μm slits a distance of 100 μm apart. Change the wavelength to 650 nm (0.65 μm) and change the y scale (slider on the bottom) to 0.6. You screen should look like the image on the right. (This is the pattern you can see from a typical red-laser physics demonstration.)

The visual display includes a graph of the actual intensity superposed on the image of what the pattern would look like. (It's in red so it might be hard to see. If you change the color of the light, you can more easily pick out the red curve on a different color background.)

It also includes a graph of the "envelope" of the graph. This is the graph of what the pattern from a single slit would look like. Since the two-slit interference pattern is occurring on top of the single slit pattern (and it changes much more rapidly), the intensity of the interference fingers runs up to the maximum given by the single slit pattern at each position. (You can see that this is the case by setting the number of slits equal to 1.)

You can make the pattern clearer by pulling the corner of the sim window out and down to make it wider. This makes it easier to work with.

## Answer these questions

1. Set the number of slits equal to 1. You can see that the intensity goes to zero at two points around the center and then it comes back a bit (but faintly) at larger distances. Why does it do this? What's happening at the positions where the intensity is 0?

2. Now put the number of slits back to 2 and look at the graph of the intensity. Since the two-slit fringe pattern is multiplied by the one-slit pattern, the intensity of a fringe to each side of the center is "squashed" to zero. Why does this happen?

3. Vary the slit width and the slit separation and describe what changing each of them does to the pattern.

4. Taking the central peak (fringe) as fringe number 0, and counting fringes out to the left or right, what is the number of the fringe that is squashed?

5. What parameters (slit width, *d*; slit separation, *a*; and wavelength, λ) control which fringe is squashed? First fix the wavelength and vary a and d. Can you write a formula for which of the fringes is going to be squashed?

6. How does changing the wavelength affect which fringe is squashed? Why?

Joe Redish 4/29/18

Last Modified: July 8, 2019