Since presentations were cancelled due to bad (possibly icy) weather, we decided to do a complete experiment to study the diffraction pattern of laser light after passing through two narrow slits. The "theory group" worked out a formula (prediction), and the "experimentalists" made the measurements and plotted them in a spreadsheet program. The theory uses the knowledge of complex numbers that we talked about at the previous meeting. "k" in the formula is an abbreviation for (2*pi/lambda), where lambda is the wavelength of the light.
Here are some pictures of the slits. The slide has 2,3,4 and 5 slits - we used the double slit because this is the easiest one to calculate. Some of the pictures were taken by pointing the camera at a microscope. Each slit is 40 micrometers (microns) wide, and the centers of the slits are separated by 125 microns.
These black&white photos show the center of the diffraction pattern at two different distances from the slits, about one meter and about three meters. The spots look the same at the further distance, except that the whole pattern is three times bigger. (The camera zoom was adjusted to make the pictures match in size.)
This is the beautiful data obtained when the detector is working correctly! The red line comes from the expression derived by the "theory group," after adjusting the height, width and position to best match the data. Now that it's clear how well the experiment is working it would be fun to get more data, covering several of the peaks.
These two plots show the expected diffraction/interference pattern calculated with a more complete theory that takes into account that the two slits each have a non-negligible width. The horizontal scale is the angle that the light leaves the slits in milliradians. In other words, the horizontal scale corresponds to +/- 50 mm on the screen, if it is placed one meter from the slots. The vertical scale (light intensity) for the figure on the left is just big enough to hold the center peak; in the plot on the right the vertical scale is increased by a factor of 20 to show better the small peaks. Note that all of the peaks have the same width - they only vary in height (light intensity).