# PHYSICS 220/230 Lab 10:  Interference and Diffraction

This week's lab introduces you to interference and diffraction phenomena. We will investigate various types of waves, including diffraction of water waves in a ripple tank. We will also use a Toolbook simulation of diffraction and interference written at Virginia Polytechnic Institute and State University and perform actual experimental measurements on a laser beam incident on two small slits cut into aluminum foil. We want to be able to explain and predict diffraction and interference phenomena and understand the strong evidence that indicates that light is indeed a wave.

### Introduction

 A Toolbook Simulation A Movie of a Ripple Tank

In order to use the Toolbook simulation to review double slit interference, click on the PySoftware icon on your desktop. Then click on the folders Toolbook, Int_Dif, and Ripple8b, and finally open Ripple.exe. Follow the simulation so that you understand the double slit phenomenon.

Click on the movie to observe how two point sources produce such a pattern in a ripple tank. The left side arrow will let you start the movie, while the two right side arrows allow you to stop and step the movie in both directions. The slider allows you to position yourself at any frame. Resizing the movie will change the frequency of the waves. Notice how each point source produces a circular wave emanating from the source. An interference pattern is obtained when these wave fronts begin to overlap. A distinctive feature of this pattern is the angles at which the waves cancel or reinforce each other. Observe these angles in the movie, and in the following movies that have different parameters, and see if you notice the similarities and differences based on lambda and slit spacing.

 d / lambda 2 d / lambda 2 d / 2 lambda

Ripple Tank Measurements

In order to determine if the water waves in the ripple tank really do obey a double slit interference relationship you must be able to determine the ratio of the source separation (d) to the wavelength (lambda) of the water waves. You will do this by printing a copy of the ripple tank from the first movie you viewed at the beginning of the lab. Find and write down its link and go directly to the movie on Entropy. Enlarge the picture and play the movie until a particularly good frame appears. Then stop the movie and use PrintKey to copy the image to Word where you can print the image. Measure the ratio of lambda to d in several orders of the pattern and find the average ratio. Be careful to always maintain the original aspect ratio, otherwise your measurements will be wrong.

### Interference Experiment

Two lab benches have been set up with helium-neon lasers and small strips of aluminum foil with double slits of various widths and separations cut into them. Shine the laser beam onto a set of double slits and observe the pattern on a white sheet of paper taped to the wall some distance behind the slits. The pattern appears to be similar to that obtained in the ripple tank with water waves. This observation seems to indicate that light is a wave, although the wavelength must be very small since we don't see the individual wave crests. If this is interference, then the pattern that you see should obey the following rules:

Do the following experiments on the double slits:

• Select a pair of slits separated by .250 mm and sketch an outline of the images that you observe on the paper. Do this very carefully so that your measurements from the paper will be accurate. On another part of the paper, repeat this process with a pair of slits separated by .500 mm.
• Measure the distance from the slits to the paper.
• Measure the separation of the maxima and minima of these double slit interference patterns on your paper after you return to your lab bench.
• Determine the wavelength of the laser light and compare (% difference) it to the known value of 632.8nm.

### Single Slit Diffraction

 Single Slit Double Slit Triple Slit

Experiment:  When a light beam passes through a single opening the beam can interfere with itself. This pattern is called a diffraction pattern rather than an interference pattern. Although the distinction between interference and diffraction patterns is often not clear cut, interference usually refers to the patterns that are produced by two or more separate sources. View the single slit movie above and observe that there are again angles at which the waves cancel. Shine a laser onto a 0.04 mm single slit and see if you observe a similar pattern. Measure the angle between minima surrounding the 0th order maximum and compare it to the simulation (see below).  View the double-slit and triple slit patterns above and see if you detect the changes that are taking place.

Measure the thickness of your hair and report your results.

Simulation:  If you look carefully at the double slit intensity pattern of the laser light or the ripple tank, you will observe a great deal of structure. A detailed analysis shows that the pattern is a combination of the simple double slit and single slit patterns. The following toolbook contains a simulation of the complete double slit that allows you to vary both the slit size and separation. This simulation can be found by clicking on the PySoftware icon and then clicking on the folders Toolbook, Runtime, Mtb30run.exe, Toolbook, and Int_Dif. Finally open Dblslitw.tbk. In order to get to the actual simulation you should click on the right hand arrow button, then click the Background button and note the mathematical description of the true double slit. Then click on the right arrow button again. The toolbook allows you to vary the wavelength, slit width and slit separation for both single and double slits. Use the Double Slit - Wide setting. Note how the patterns change as different variables are selected. Simulate the 0.04 mm single slit.   Compare your the simulation results to what you observed.

Print the Toolbook simulation. Use PrintKey to capture a picture of a particularly good pattern. Then copy the screen into Word. Edit the picture by right clicking on the mouse and showing the Picture Toolbar. Then use image control to make the picture black and white rather than gray scale. This will save toner when you print the picture for your notebook.