Notes for Experiment #9 -- Physical Optics

Notes & Hazards

1. Notes on the Theory part:
• Interference

Remember that waves interfere destructively when they are out of phase (e.g., E+F=Z in Figure 1 on p. 102); they interfere constructively when they are in phase (e.g., A+B=X in Figure 1 on p. 102). Remember, that in order to have total destructive interference between 2 waves of equal amplitude and wavelength, they must be 180o (or l/2) out of phase.

• Single Slit Diffraction

Diffraction is the bending of light around corners. Diffraction effects occur for all kinds of waves but are only apparent when the size of the object is on the order of the wavelength. For today's experiment, remember that the dark bands are labelled consecutively for the single-slit (see diagram below; the blue, rectangular boxes represent the actual band of light you'll see, interspersed with the dark spots representing destructive interference). Notice that the dark bands are consecutively labelled for single-slit diffraction and that y1, the distance from the center of the central bright band to the center of the first dark band, is simply y1 - yo; similarly, the distance to the 2nd dark band is just y2 - yo; etc.

To see how they get EQ5 on p. 104 (tan a = y/L), refer to the figure below: Here, the tangent is simply the opposite/adjacent which is equal to y/L.

• Double Slit Diffraction

Double slit diffraction is represented very well by Fig. 4 on p. 105. Here, please remember that the labelling of the dark and bright spots is intermixed (see labelling of the y's in Fig. 4). The pattern you'll actually see on the screen is illustrated below (the blue boxes represent the light bands in the actual spectra you'll most likely see): 2. Notes on the Procedure part:
• The theory is really nice to understand but in order to do the lab, you really only need to use 2 equations (although it would be nice to understand them also, wouldn't it?): use EQ 6 for the Single Slit part (remember, n=1,2,3,... for the dark spots here) and use EQ 13 for the Double Slit part (remember, n=1,3,5,... for the dark spots here). Also, please keep in mind that n is just the index for the y's; so y1 has n=1, y2 has n=2, etc.
• Section 4.1, p. 108:
• Make sure you measure the fringes from the center of the central bright spot to the center of the dark area, as per below: • The metallic side of the slit (the one without any labels) is the one you want to shine light on.
• For Step 2: Keep your setup on the optical bench so feel free to use a distance smaller than 1.5m (as long as it's more than about 1m).
• Section 4.2, p. 108: For the double slit experiment, try to shine the laser as directly as you can on the two slits. This will help determine how good your interference pattern is and hence how good your numbers are. The double-slit interference setup assumes that plane, monochromatic waves will be impacting both slits equally; however, if the pen laser isn't oriented exactly right, the laser beam will most likely strike one of the slits more than another (and it might be directed up or down, too). The slit that gets hit preferentially will probably display a diffraction pattern (since it's a single slit being hit by light, it'll demonstrate the same kind of diffraction pattern as you saw in Section 4.1 above). In this case, instead of having one solid central block of light, you'll have a central block that's made up of many smaller blocks (the diffraction pattern from the single slit). The idea is to orient the laser and the slit to minimize the contribution from this extraneous, single-slit diffraction. So if you see a whole lotta little blocks within your big blocks, mess around with the orientation of the laser and the slit until you've brought it down to a minimum. Once done, you can calculate the y's as below: • Section 4.3, p. 109: No experiment here; just simple calculations. One partner can work on this while the other sets up the next part (the only tricky thing about Section 4.4 is the setup; the data-gathering itself is quick and straight-forward).
• Section 4.4, p. 110:
• Be sure to unhook the resistor when you're done with the experiment (this is to keep from bleeding the battery).
• The photo-diode's input is on the opposite side to the banana plug inputs and the battery.
• Start off with the initial position of the diode assembly being 5cm from the screen. Also, make sure everything's lined up to the same height (i.e., the spot/dot created by the laser on the screen, the photo-diode's input, and the pen laser should all be at the same height).
• For this part, make sure you keep the laser and the screen fixed BUT keep the photo-diode assembly free to move so you can gather the data at different distances.
• How can knowing the Voltages give us how many photons there were per second (i.e., the intensity)? Well, we know that Vlaser - Vno laser = DV = DEd = DIR and since I is equivalent to the number of electrons flowing by per second (and we know that 1 electron gets knocked out for each photon that hits the diode), we essentially get the intensity.
• A really nice link that talks about solar cells, interference, diffraction, etc.

Corrections

1. Minor errors only.

Required Materials:

1. Laboratory Manual (SGM 407)