To use a laser to count the number of lines on a CD.
Set up the laser light source and the target grating (e.g.: the “rainbow” side of an audio CD) as shown in the diagram below. The screen or wall must be perpendicular to the grating on the table. Use a very low angle of incidence for the light source—somewhere around 5 and 20 degrees. (Keeping a shallow angle lets you ignore angle measurements for the calculations that come later.)
Turn down the lights in the room, switch on the laser and rotate the grating until you get a series of red laser dots on the wall, blackboard, a sheet, or anything perpendicular to the table. You might want to put marks on this screen later when you do the measurements. You may have to rotate the laser in the stand and generally fiddle with things to get it right.
The first dot on the wall is called the “specular” dot and is just the direct reflection of the laser beam from the CD. The rest of the dots above it are caused by diffraction so you start the numbering from the first one of those. The specular spot is the “zero” spot. You might have to adjust the angle of the incoming laser light to get the series of dots to appear. By the way, you need a laser light source for this experiment because laser light is collimated which means the light is all nicely straightened out into a solid beam. Note that Brockhouse had to use collimators in his neutron spectrometer. Neither your experiment nor Brockhouse’s will work without collimated beams.
After you can see the dots you need to make a few measurements. First of all, you must establish the baseline, which is the place on the screen that is the same height as the top surface of the CD on the table. Draw the baseline on the wall. Measure the following:
L (The length from the laser spot on the CD to the wall or projection screen.) __________
ho (The height from the baseline to the lowest red spot on the wall.) __________
h1 (The height from the baseline to the second red spot on the wall.) __________
h2 (The height from the baseline to the third red spot on the wall.) __________
h3 (The height from the baseline to the fourth red spot on the wall.) __________
...and any other dots you want. (Note: if you only get h0 and h1 that’s enough)
You also need to know either:
l (lambda, the wavelength of the laser ) __________
d (the spacing of the grating) __________
If you know the number of lines in the diffraction grating (or CD), you can infer the wavelength of the laser light. If you know the wavelength, you can figure out how many lines in the grating. Use the formulas:
In Brockhouse’s triple axis spectrometer he could make these measurements in 3 dimensions, plus he also measured the shift in energy of the neutron beam which told him more about the vibration of atoms within solids. Using similar techniques, solid state physicists employ beams of radiation to measure physical properties like the spacing of atoms within crystals.
In your experiment, try turning the grating 90 What happens to the dots on the screen? If it makes you curious why they form an arc, you might want to find out more about solid state physics.