L19. 

For your report:  In addition to the usual heading and goals, include items below as indicated in red.  You'll fax your report, since you'll need to include your tracings.

Goals:  

• to measure the wavelength of laser light using the Young's double slit method

• to use the measured wavelength to measure the track spacing on a CD

• to compare the interference patterns obtained from single, double, and multiple slits and to interpret the results obtained

Required reading:

• For Part A, sections 28.1 and 2.

• For Parts B and C, sections 28.4 and 6.

Preparation:  Collect the following equipment.

Single, double, and multiple slits on a piece of transparency film  [These will be mailed to you. However, you can also print your own. Open this file in a photo-editing program like Paint or Adobe Photoshop. Print the file first on paper to make sure it prints correctly. Use at least a 600 dpi printer. The size of the image on the paper should only be 1" x 2". If it's printing larger, that's because your application is changing the resolution of the image. (Web browsers will do this.)  Be sure to print from an application that maintains the image resolution. Photo-editing programs will generally do this. Once you've figured out how to get the image to print at 1" x 2", print it on transparency film.]
Laser penlight

Meter stick

Tape measure (optional)

CD (blank or burnt)

Ring stand and clamp (to hold CD)

1 sheet of black or dark construction paper (to be used to shield part of the CD)

scissors

sticky tape

It's best if you can do the experiment in a very dark room.  You'll also need to have someone assist you.

Identification of the slits:  The slits are numbered on the transparency film.  Here's information about them.

Here's how the measurements given above were made.  First, a file with a resolution of 600 pixels/inch was created.  Narrow white lines were drawn on a black background.  All of the lines for the double and multiple slits were 1 pixel wide.  That works out to (1/600 in)(25.4 mm/inch) = 0.0423 mm.  The single slits were 3 and 5 pixels wide.  Separations for the double and multiple slits ranged from 2-4 pixels.  Separation were measured from the center of one slit to the center of the next.

Method

Part A.  Wavelength of Laser Light

Note:  In recording measurements, identify quantities with the same symbols as are used in the text in section 28-2.

The method is fundamentally like that of Young's experiment described in section 28-2.  You have the advantage, though, of being able to use a laser and digitally-created slits.  An overhead view of the experimental arrangement is shown below.  You'll need to work in a room that can be darkened, since the interference fringes are faint.

Here are some design considerations:

• If you hold the double slits vertical, the pattern of fringes on the wall will be spread horizontally.  If you hold the slits horizontal, the fringes will be spread vertically. 

• You'll need a way to hold both the double slit and the laser steady while taking measurements.  We leave it to you to find a way to do this.

• The double slit needs to be 4 to 5 m from a wall in order to provide distance for the interference pattern to spread out.  This will make the fringes wider, and you can measure them more accurately.

• Tape a sheet of typing or copy paper to the wall in the area where the interference pattern appears.

Now here's what you do.

1. Use the double slits marked 1 (d = 0.127 mm).

2. Turn off the lights and shine the laser through the slits in order to cast the interference pattern on the paper taped to the wall. Be sure to align the laser with the slits.  One way that works is to hold the slits vertical and then slowly scan the laser horizontally, sweeping through the double slit as you do.  You're looking for a pattern of faint red fringes on the wall.  It will look something like the photo below.  The fringes will be about 1-2 cm apart.

3. With a pencil, trace the outline of the fringes onto the paper.  Also, clearly mark the positions of the center of the central bright fringe and the centers of the two dark fringes on either side of the central bright fringe.  Beside the tracing, write the slit separation to distinguish it from the next tracing that you'll do.

4. Shift the paper up or down a few inches to provide a clear area for your next tracing.  Using the double slits marked 2 (d = 0.169 mm), repeat steps 2 and 3.

5. Measure the distance from double slit to wall to the nearest centimeter.  Record this distance on your tracing.

Now you're ready to take measurements from your tracings.  Do the following for each of the two tracings.

1. Label the maxima (bright fringes) m = 0, m = ±1, etc.  See the example tracing below.

2. Examine Example 28-2 in the text to see how the wavelength is ideally determined.  We use the term ideal, because in practice the fading in intensity of the fringes away from the central fringe makes it difficult to determine fringe spacing.  You'll need to make a decision about what distance (or distances) to measure to use for your calculation of the wavelength of the light.  Clearly indicate on your tracing what distance (or distances) you measured and record the values.

For your report:  Describe in paragraph form your method for positioning the laser and the double slits and holding them steady, for measuring the distance from slits to screen, and for measuring distances from your tracing.

Analysis for Part A

For your report:  Include answers to the following questions.

1. Draw a diagram on which you label all the distances that you'll need to calculate the wavelength.  Label them in symbols rather than numbers.  (Don't worry about calculating the angle, q.  Do you see why you don't need to know what it is?) 

2. Now calculate the wavelength for tracing 1.  Convert your result to nanometers, which is the conventional unit for the wavelength of light.

3. Calculate the wavelength for tracing 2.

4. If your laser has the wavelength written on the label, give that number.  If not, give the color of the beam.  Then do a search on the internet for the wavelengths typical of laser pointers.  The phrase wavelength laser pointer is a good search phrase.  Give the results of your search and cite your source by URL.

5. Compare your values for wavelength from the two tracings.  Of course, they should be the same, but experimental errors influence results.  Qualitatively discuss potential sources of error that would contribute to differences in your values of wavelength determined from the two tracings.  (Don't discuss errors that would influence both calculations in the same way.)

6. Now discuss any additional sources of error that would cause your values of wavelength to differ from accepted values.

7. Report your values of wavelength in Assigned Discussions.

Part B.  Track spacing of a CD

The tracks of a CD are very closely spaced and can be used as a reflection diffraction grating.  (See section 28-6.)  Now that you know the wavelength of the light from your laser, you can use that information to measure the CD track spacing.  Do the following to set up for the measurement.

1. Lay your CD on a piece of construction paper (actually, most any paper will do) and trace around it.  Then cut out the tracing.  This will be a mask for the CD.  Cut a slot about half a centimeter wide along a radius of the mask.  Cover the track side of the CD with the mask and tape the edges to the CD in several places.  The final result should look something like the diagram to the right.

2. Now arrange the CD and laser as in the diagrams below.  Both side and overhead views are shown.  If you don't have a ring stand, tape the CD to some kind of vertical support such as a book stood on end.  You can hold the laser by hand, but it will be easier to keep the interference pattern steady if you can set the laser on something.  Aim the laser at the exposed portion of the CD's surface.  Position the laser so that it doesn't block the interference pattern. A wall will serve as your screen.  Note that unlike Part A where the slits were 4-5 m from the wall, the CD need only be a meter from the wall.  You'll know why when you see the diffraction pattern.

Side view	Overhead view

3. Remembering that your goal is to measure the track spacing on the CD, take all the measurements you need in order to achieve that goal.  Record your measurements with labels.

4. Clearly describe how you made your measurements in step 3.  Your descriptions must leave no doubt in the reader's mind what you measured and how you measured.

Analysis for Part B

1. Starting with the appropriate formula, calculate the track spacing of the CD.

2. Do a search on the internet for the value of the track spacing on a typical CD.  State the value and give the URL of the source.

3. Calculate the percentage difference between your calculated value of the track spacing and the value you found in your search.

Part C. Comparative observations

For your report:  Include the table as described below.

The method of the experiment is simple.  Position yourself 4-5 m from a light-colored wall as you did in Part A. You can tape white paper to the wall in order to have a plain, white background.  Shine the laser through each of the 6 sets of slits in turn.  Examine the interference patterns from all of the slits before writing anything.  Then examine each pattern once again and record comparative observations about the brightness, sharpness, and separation of the fringes.  By comparative observations, we mean that you are to rank the slits on a numbered scale according to the property under consideration.

Record your observations in a table like the one below.  You may copy the table into a Word document if you wish.  However, you'll have to print it out for faxing.

In the top row, define the scale that you will use for ranking. Make it clear what number represents the greatest value of the property in question. Note that the same number must represent the same amount of the property in question (separation, brightness, sharpness) whenever used. For example, if you determine that the fringe separations for two different slits are the same, then you must rank them with the same number.

There's also a column to write the condition--in equation form--for constructive or destructive interference.  Look these up in the text if you need to.  The formulas must be in terms of wavelength, slit separation (or width), angle q (as defined in the text), and order (m).  In addition to writing the equation, indicate the values of m for which the formula applies, and indicate whether the condition is for constructive or destructive interference.

Analysis for Part C

For your report:  Include responses to the following.

1. Sketch graphs of intensity as a function of position on either side of the central maximum for slits 1, 4, and 6.  We pick these because they provide for comparisons for single, double, and multiple slits of the same width or separation.  Draw the graphs with the same position scale for visual comparison of fringe separation and sharpness.  If, for example, two of the sets of slits have maxima of the same order at the same position, then your graphs must show that.  If one set of slits has fringes much narrower or brighter than another set, your graphs must show that.

Click on this link to open a page with three sets of axes.  Print the page and draw your graphs on it.  A position of 0 represents the position directly opposite the slits on the screen.  This would, for example, be the center of the central maximum for a double slit pattern. Use the dashed lines to help line up features of the graphs that appear at the same positions.  Draw neatly and make the largest peaks use the full intensity scale. Make sure that distinguishing features of the graphs are clearly visible. Use your textbook as needed for help in drawing the graphs.

2. We're sure you noticed that the interference patterns for the multiple slits were much sharper than for single or double slits.  For the CD, in fact, the fringes were just spots separated by large regions of darkness.  The textbook doesn't explain why the multiple slits are so much sharper.  Do a web search to find an explanation for the fact that with more slits, the fringes are sharper.  Cite the URL as always.  If you use any text from the site verbatim, enclose it in quotes.