Things You Will Need
Go ahead and run the PhET simulator in another window, as you have twice before. You will also need a small ruler (this part of the simulator doesn't come with a virtual tape measure!).
While it is certainly not required that you do so, you may find this entire lab (or maybe part of it) to be fun to do yourself at home! You can do these if you happen to have a laser pointer, and have a way to look up its wavelength. You will also need a compact disk or DVD, a tape measure, some tape, and bit of space to work with. Notes on doing this lab at home are in red for your convenience.
Using the Simulator
Here is the configuration of the simulator you will need:
- select the window "Diffraction"
The large black square on the left with a white circle in it is the barrier to the light, and the white circle is the aperture through which the light passes. The other black square is the screen onto which the diffraction pattern in is projected. We will want to simulate a thin rectangular aperture (actually a thin rectangular barrier, but we'll get to that later), so:
- click the rectangular aperture button
- elongate the aperture to its maximum by dragging the "Height" slider to 0.40mm
- turn on the laser by clicking the circle
The wavelength of the laser and the width of the gap are left as variables for use to play with. Note that the scale lengths for both the slit and the screen are given on their upper-left corners, and they are not the same. Measurements of the slit are unnecessary, as the gap width is given in the "Width" slider, but measurements of the diffraction pattern will require a ruler and the scaling provided.
In order to use the simulator to mimic the case of our real-world physical experiment, we will need to make sure every dimension matches. We can adjust the gap width and make measurements of the diffraction pattern, but the distance from the slit to the screen is also important, and that is not given (we are not given a scale for the top of the diagram, so we can't measure it with a ruler). So to that end...
- Use any wavelength and gap width you like to find the distance from the slit to the screen, then confirm your calculation with a new wavelength and gap width.
The Thickness of a Human Hair
In the text references for the Background Material is a discussion of Babinet's principle, which essentially states that under the right conditions, a thin barrier to a laser beam results in the same diffraction pattern as a slit of the same width. We will exploit this to measure the thickness of a human hair.
If you are doing this at home, you will of course need a hair that you can place into the path of the laser beam. The simplest way to do this is to tape it across the hole in the laser pointer where the beam emerges. BE CAREFUL NOT TO LOOK INTO THE LASER WHEN DOING THIS, AS ACCIDENTALLY TURNING ON THE LASER CAN DAMAGE YOUR EYE. You'll know the hair is in the beam when looking at it from the side, you see a bright "bead" where the hair is (see the pictures below). Then point the pointer at the wall from the distance that you computed in question #1 above. You should see a diffraction pattern similar to the (horizontal) pattern shown in the simulator, and you can make direct measurements of the diffraction pattern.
Figure 5.2.1 – Hair in Laser Beam
The hair in the pictures above has been taped across the hole of a compact disk (which, efficiently, is used for another purpose later in this lab), but any manner of getting the hair into the beam is sufficient. The hair is vertical, like the rectangle in the simulator, providing a horizontal diffraction pattern:
Figure 5.2.2 – Diffraction Pattern
There is a lot of stray light here, but the "speckles" can be ignored, and we need focus our attention on the bright horizontal bands that constitute the hair's diffraction pattern.
Taping the hair across the opening of a laser pointer may or may not exhibit this much "noise" in the diffraction pattern, but much will depend upon the quality of the laser.
The distance to the screen from the hair was adjusted to be the same as that of the simulator, and a measurement was made of the distance between the two dark fringes that bracket the central bright band. The wavelength of the laser is also known:
- distance between first-order dark fringes \(=1.6cm\)
- laser wavelength: \(\lambda = 633nm\)
- Use the simulator to approximate the thickness of the hair. This may require a bit of trial-and-error to get the dark fringe spacing to the correct value. Perhaps meticulously placing some tape on your monitor with the proper spacing will help? Take a screen shot of the simulator when you feel you have reached the correct value and attach it to your lab report.
- Mathematically compute the hair width using single-slit diffraction formulas. Justify any approximations you might use.
If you check the thickness you get at home against what is computed in the "packaged lab" here, don't be discouraged if they diverge from each other substantially – hairs come in a pretty wide variety of thicknesses!
The Groove Density of a Compact Disk
Next we will use our laser and the parallel that we drew between diffraction gratings and reflections off surfaces with regularly-spaced grooves to determine the density of grooves (number of groove per centimeter) on a compact disk. To do this, we need to set up the laser to reflect off the CD, and have the reflection illuminate a wall a distance away.
Figure 5.2.3 – Reflecting Laser Light Off a Compact Disk
Figure 5.2.4 – Bright Fringes Off Compact Disk
Note that the laser strikes the CD on the grooved side (naturally), at a point located horizontally from its center. In this region, the grooves will be oriented vertically, so the fringes will spread horizontally. You may be able to see the second-order fringes as well – if so, this can reduce the overall uncertainty in your result.
Now for the measurements made in the lab:
- distance from CD to wall \(=230cm\)
- distance from central bright fringe to:
- left bright fringe \(= 98cm\)
- right bright fringe \(= 100cm\)
- Compute the density of grooves in the compact disk, measured in grooves per millimeter. [Make a note that these bright fringes do not occur at small angles, so you need to take care not to use any approximations that assume this!]
Download, print, and complete this document, then upload your lab report to Canvas. [If you don't have a printer, then two other options are to edit the pdf directly on a computer, or create a facsimile of the lab report format by hand.]