Week 10: Single and double slit diffraction

This week's lab introduces a new tool, Video Point. Video Point allows you to take position data from individual frames of a movie. By combining the data from a series of frames you can study the time evolution of phenomena. You will use it to study diffraction of water waves in a ripple tank. This video analysis will be combined with a Toolbook simulation written at Va. Tech. and actual experiments of a laser beam incident on two small slits cut into aluminum foil. In your lab report you should:

• explain and predict diffraction and interference phenomena and
• provide strong evidence that light is indeed a wave.

You may include screen shots of any Toolbook simulations in your lab report.

We are near the end of term and I feel like this class had had to suffer a bit learning new technology and putting up with various hardware/software problems. You have also been asked to do more writing that traditional physics labs. You payoff is coming. There will be only two additional laboratories after this lab. There should not be any laboratories after Thanksgiving to give you time to prepare for final exams.

Introduction

Due to copyright, the following can can only be run from the Physics Department network.

A Toolbook Simulation	A Movie of a Ripple Tank

Click on the Toolbook simulation to review double slit interference; click on the movie to observe how two point sources produce such a pattern. 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.

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 to the wavelength of the water waves. You will do this using the Video Point software described in the next section.

Video Point

D/lambda	2 D/lambda	2 D / 2 lambda
Single Slit	Double Slit	Triple Slit

Video Point is a general purpose video analysis tool that allows you to analyze the motion of objects in digital movies. Think of VideoPoint as a movie viewer coupled to a data table. Every time you start click the mouse the x,y coordinates are entered into the table. This software was designed for (and written by PHYSICISTS) so video point does the types of analysis physicists like to do. It is not very good for viewing Jurrasic Park.

VideoPoint can:

• make measurements using a scale that you control. If you can find an object of known length on any frame of the movie you can scale all your x,y coordinates.
• translate the origin, i.e., move the axes, anywhere inside the movie. Remember that physics shouldn't depend on the choice of origin. Choose an origin that makes sense for the problem. You can do this at any time and all your previous x,y coordinate measurements will update their values automatically.
• rotate the axes. Coordinate measurements update automatically.
• switch from cartesian to polar coordinates.
• plot the positions of objects as functions of time, i.e., frame number. If you need to do more complex analysis, export your data to a spreadsheet.

Learning to use video point is well worth the effort but if you would rather do the following exercises without video point you may. Just print out screen shots, get out a ruler and a protractor and measure the slit separation, wavelength, and angles. Read on if you think there is a better way.

Video Point Instructions

The first introduction to VideoPoint is usually in mechanics where a typical experiment requires that the center of mass of an object be located on each frame of a movie. The center of mass motion can then be plotted as a function of time. The default behavior of VideoPoint assumes this scenario so you may want to change some of the preferences before you take data.

Start Video Point and open the DblSrc2.mov file in the movies directory. Since you will be measuring the position of the interference minima and there are approximately 6 minima visible, you should type 6 into the dialog box asking for the number of features to me measured on each frame. Click the OK button. Starting from the left, click on each of the 6 minima visible on the first frame. What what happens with each click particularly the 6th click. Each time you click data is added to a table giving the x,y coordinates of your click. On the 6th click the movie advances to the next frame. Repeat the process. Don't worry if the clicks are not perfect. You can adjust them later. Stop after you have taken data on 4 or 5 frames. (If you were studying the motion of an object you would probably continue clicking until you reached the end of the movie.) You have all the data you need so go to the main menu and click on the Options item and turn off the AutoPointAdvance and the AutoFrameAdvance feature.

More to come.

Interference Experiment

Two lab benches have been set up with lasers and small strips of aluminum foil with single and double slits. Shine the laser beam onto these double slits and observe the pattern on a white sheet of paper some distance behind the slits. The pattern appears to be similar to that obtained in the ripple tanks 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.

Do the following experiment:

• Sketch the patterns that you observe for various configurations.
• Measure the distance to the paper and the positions of the maxima and minima of the double slit interference pattern.
• Determine the wavelength of the laser light.

Single Slit Diffraction

When a light beam passes through a single opening the 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 patters 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 and observe that there are again angles at which the waves cancel. Do the following:

• Observe the movie.
• Sketch the intensity behind the slit. Try and estimate the intensity from the shadow contrast in the movie.
• Look up the relationship between the wavelength, the slit size, and the angle for the first minimum in the pattern. Determine if the pattern in the movie obeys this relationship.
• Compare this relationship to a similar relationship in the double slit interference pattern.
• Shine a laser onto a single slit and see if you observer a similar pattern.

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. At 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. In order to get to this simulation you should click on the Background button of the opening screen and then on the arrow button near the lower right hand screen. Move the sliders to values that correspond to you laser light experimental settings and then plot the results. How does the plot compare to you experiment?

Print the Toolbook simulation. In order to get the print menu press the F3 key while the toolbook is active. You will get an error message about not being able to enter author mode. Ignore this message. Notice that you now have a new menu at the top of the screen. Print is in the usual place under the File menu item.

Reference to the Multimedia Toolbook

Sections of the Virginia Tech Toolbook have already been used in this lab. This section provides a reference to the complete Interference Demo-Media Toolbook for the interested student.

The MultiMedia Toolbook viewer should already be configured as the helper app for *.tbk files. Ask for help if the "configure viewer" dialog box appears when you click on toolbook hypertext anchor.

Note: Not everything may work in the following demo. Remember that we are adapting software that was developed at another school for different equipment. For example, we do not have the live video so clicking on the little motion picture camera won't produce the expected result. Windows 95 has also created a "bug" in Dr. Long's and Dr. Bowden's software. Whenever a multimedia document calls another multimedia document the second document will not open automatically. Don't worry about this bug. Just return to this page and click on the link to the toolbook document in the summary below and you will be able to view it.

Reference to the Interference and Diffraction Toolbook.

Complete Double Slit

• Background
  • Interference Factor
    • Min/Max
    • Intensity
    • Geometric Derivation: Phasors
    • Analytic Derivation
  • Diffraction Factor
• Apparatus.
• Demonstration: Run an actual experiment. Won't work without Dr. Long's and Dr. Bowden's toys.
• Summary