Physics Lab
Diffraction
1
CAUTION: NEVER LOOK DIRECTLY INTO A LASER BEAM, AND DO NOT POINT
THE LASER AT ANYONE ELSE’S EYE
Note: Since this is the first time this lab has been performed here, you are encouraged to make
suggestions to improve the process, either to make it easier, or to make it a more effective learning
experience. These sorts of comments should go in the conclusions.
Part 1: Determining the wavelength of your laser
For this part, you will use a laser, a diffraction grating, an optics bench, a screen (onto which you
will tape some scratch paper), a small ruler, and a mass set. You may use either a laser pointer, or a
Helium-Neon tube laser.
For a diffraction grating, constructive interference happens when dsinθ = mλ (where m=0, ±1, ±2,
etc.).
1.
d is the separation distance between the separate slits/grooves. You will assume that the
information printed on the slide is correct, in giving the number of grooves per millimeter. Use
this to find d.
2.
Attach the screen to the track as in the previous lab. Place the laser on the other end of the
track, using your textbook or some other convenient object to raise it to an appropriate height.
3.
Place one of the masses (the 500 g mass often works well) on the track, and lean the grating
against it, so that the grating is nearly vertical, and is perpendicular to the laser beam. Make
sure the laser beam passes through the grating, and that the diffraction pattern that is formed is
clearly visible on the screen.
4.
Tape a piece of paper to the screen. Make sure the central bright peak and at least two peaks to
one side are clearly visible on the paper. (You may need to move the grating closer to the
screen to accomplish this.) Sketch the bright points on the paper. Be sure to note on the sketch
which dot is the central bright peak.
5.
Using the track’s rule, measure the distance from the grating to the screen, and note your
uncertainty in that measurement. Note that the distance from the laser to the screen is not
needed for anything.
6.
Remove the paper from the screen, and measure the distance from the center of the central
bright point to the center of the first bright point, and from the central bright point to the
second bright point. Be sure to note uncertainties with each measurement. (Note: it is very
difficult to be more precise than the diameter of a dot itself, though your own uncertainty may
be somewhat greater depending on how confident you are in your sketch.)
7.
Use trigonometry (not the small angle approximation), to determine θ for each of the side
points.
8.
Use dsinθ = mλ to find λ from each of the side points. Be sure to use uncertainty throughout at
least one calculation.
9.
Calculate the % difference between your two λ values.
10.
For parts 2 and 3 of this lab, you will use an average of your two values as your laser’s
wavelength.
Physics Lab
Diffraction
2
Part 2: Determining the thickness of a human hair
In addition to the equipment you used for the previous part, you will also need an index card with a
hole cut in it, some tape, and a human hair.
It is possible to prove that, at large distances, the shape of the interference pattern formed by a single
obstruction is the same as that formed by a single slit (one application of Babinet's Principle). In
single-slit diffraction, destructive interference happens when asinθ = mλ (where m= ±1, ±2, etc.).
1.
Take a piece of hair, and tape it across the hole in your index card. Remove the grating, and
put this card in its place, so that the hair is nearly vertical, and is perpendicular to the laser
beam. Make sure the laser beam passes across the hair, and that the diffraction pattern that is
formed is clearly visible on the screen. Make sure you can clearly identify each of the minima.
You may need to move the hair farther from the screen to accomplish this.
2.
Tape a piece of paper to the screen, and sketch the pattern that appears. Be sure to note on the
sketch which region is the central bright peak.
3.
Using the track’s rule, measure the distance from the hair to the screen, and note your
uncertainty in that measurement. The distance from the laser to the screen is still not needed
for anything.
4.
Remove the paper from the screen, and measure the distance from the center of the first dark
region on the left, to the center of the first dark region on the right. One-half of this value will
correspond to the “y” for the first dark line. Also measure the distance from the center of the
second dark region on the left, to the center of the second dark region on the right. Be sure to
note uncertainties with each measurement. (Note: this measurement will likely be more
uncertain, because it is hard to judge exactly where the destructive interference is strongest.)
5.
Use trigonometry or the small angle approximation (whichever seems most appropriate), to
determine θ for each of the side points.
6.
Use asinθ = mλ to find a from each of the side points. Be sure to use uncertainty throughout at
least one calculation.
7.
Calculate the % difference between your two a values.
8.
Using the micrometer calipers, measure (as best you can) the diameter of this hair. Again, be
sure to note the uncertainty in this measurement.
9.
Calculate the % difference between the value you measured using the calipers, and the average
of the two values you found via diffraction.
Part 3: Determining the track spacing on a CD
In addition to the equipment you used for the previous part, you will also need an index card with a
small hole punched in it, a magnetic end stop, three magnets, and a CD.
Diffraction gratings can be made by multiple parallel grooves affecting reflected light, not just
transmitted light. Audio and computer CD’s are one common example. The spectrum of colors you
see when holding them up to standard lighting comes from the fact that different wavelengths are
diffracted at different angles. As before, we will use the fact that constructive interference happens
when dsinθ = mλ (where m=0, ±1, ±2, etc.), for a diffraction grating.
Physics Lab
3
Diffraction
1.
Remove the card and piece of hair, and the mass it had been standing on. Stick the card with
the small punched hole to the magnetic end stop (using 2 magnets), and mount it on the track.
The card should be nearly vertical, and the laser beam should pass through the hole. This may
be tricky; feel free to use masses, stacks of paper, etc. as necessary in order to allow the laser
beam to pass through the hole.
Aim
2.
Stick the CD to the screen using a magnet, with the grating side of the CD
facing the laser. You want the reflection from the CD to hit the index card.
In order for the diffracted points to fit on the card, the laser should hit the
CD near an edge whose tangent is nearly vertical.
3.
On the punched index card, sketch the bright points. Be sure to note on the
sketch which dot is the central bright peak. Make sure to have the central
bright peak and at least two peaks to one side, clearly visible on the sketch. In order for this to
happen, the central bright point must not be reflected right back through the hole.
4.
Using the track’s rule, measure the distance from the CD to the index card, and note your
uncertainty in that measurement. Once again, the distance from the laser to the screen is not
needed for anything.
4.
Remove the index card from the screen, and measure the distance from the center of the central
bright point to the center of the first bright point, and from the central bright point to the
second bright point. Be sure to note uncertainties with each measurement. (These may be
quite large, especially if the card was not flat.)
5.
Use trigonometry or the small angle approximation (whichever seems most appropriate), to
determine θ for each of the side points.
6.
Use dsinθ = mλ to find d from each of the side points. Be sure to use uncertainty throughout at
least one calculation.
7.
Calculate the % difference between your two d values.
Laser
Here
Questions:
1.
The laser pointers claim to have a wavelength between 630-680 nm. The Helium-Neon lasers
are expected to have a wavelength of 632.8 nm. Do your answers for wavelength surprise
you? (Are they more accurate than you expected? Less accurate?) Why or why not?
2.
Why does the pattern formed by the hair in the laser beam have a bright, rather than dark,
center?
3.
What were the most likely reasons for the difference you found between the width of the hair
measured via diffraction, and the width measured using the calipers?
4.
For at least two calculations where you did not use the small angle approximation, try using the
small angle approximation to determine θ. Is there a significant difference? Why or why not?
Note: for all calculations of uncertainty, use the “worst case” high/low/expected method. If you
have questions about this, please ask in class.