# Use diffraction to measure wavelength of light (and width of hair)

Your job is to use a diffraction pattern to determine the wavelength of light emitted by a laser. If you have time, you can then measure properties of human hair.

Set up an optics bench, laser, and Single Slits wheel as shown. Place a piece of paper on the wall, so that the distance L is about 1.5 meters.

1. You should be able to find positions on the wheel which have single slits of width a =
1. 0.02 mm
2. 0.04 mm
3. 0.08 mm
4. 0.16 mm

2. For each position, shine the laser through the slit and onto the screen. Pick a pair of DARK spots which are an equal distance to the side of the center and easy to see. Good choices might be the first, or fourth, or tenth spot to either side of the center -- it will vary with the slit width. Measure the separation between these two spots.

In the example above, Joe is measuring the distance between the m = 4 DARK spot to either side of the center.

3. Make a table of your measurements. Be sure to include the width of the slits, the index of the spots you measured, and the distance y of each spot from the center. Don't forget the units!

4. Now, compute the wavelength of the light. You have several choices:
1. Good: pick one measurement, write down a formula, apply the formula.
2. Better: use each set of measurements to compute a wavelength, the find an average wavelength and estimate of its uncertainty.
3. Best: make a graph which uses all your measurements to find the wavelength (and uncertainty). Use the equation
```                                (  L * m   )
y   =  lambda *  ( -------- )
(    a     )
```
and choose quantities for your axes so that the slope of the line on the graph is the wavelength lambda.

How does this measurement of wavelength compare to the measurement you made using two slits? Do they agree within the uncertainties?

#### Are blonde hairs thinner than dark ones?

If you have time ...

Pick one member of your group. Pluck three hairs from its head, and use diffraction (plus the wavelength you've determined already) to calculate the width of each one. Compute the average and standard deviation of these widths.

Write your results on the board at the front of the class. Indicate whether the hair is light or dark in color.