Physics 309 Lab 3. where the small angle approximation has been used. This pattern has maxima at. Y Max. n L /d (2)

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1 Physics 309 Lab 3 Introduction This will be a lab whose purpose is to give you some hands-on experience with optical interference and diffraction, using small green diode lasers as the light sources. Each laser is equipped with a beam expander lens, which makes alignment easier The basic 2-slit geometry is reproduced below Plane wave y k D d d sin( ) L As a reminder, for two slits, the intensity pattern is I [cos(k /2] 2 [cos( dy / L)] 2 (1) where the small angle approximation has been used. This pattern has maxima at Y Max n L /d (2) When there are more than 2 slits, we use the N-slit formula for the interference pattern: sin(nk /2) I sin(k /2) 2 (3) which has principal maxima that are also determined by Equation (2). Diffraction effects for a single slit of width D yield 1

2 2 sin(kd /2) I kd /2 (4) and for multiple slits of width D and separation d one should observe the product of equations (3) and (4). WARNING: While these low-power lasers are designed for classroom use, it is NOT a good idea to shine them in your own or other people s eyes. Try to keep both your incident and scattered beams in a plane near the desktop, and then keep your head out of that plane. Set up your apparatus with the slide close to the laser, and arranged so that the main reflected beam is blocked by the body of the laser. Turn the laser off when not measuring with it i.e. when doing calculations. PART 1 2-Slit Interference Using the green laser, set up and observe 2-slit interference patterns. You should start with the Cornell plate (large glass plate). A diagram of the layout of this plate is given at the end of this handout. It has several two-slit patterns you can use. NOTE: The Cornell plate has a cryptic notation, and an obscure measurement scheme. The green diode laser s wavelength is = 532 nm. Use that to verify what the slit-spacings actually are on the Cornell plate. Arrange your experiment so that your interference pattern shines on the square projection screen with white paper on it. This way you can mark the position of the interference maxima with a pencil, turn off the laser, and measure their spacing with a ruler. You may want to tape additional paper to the wall. (don t write on the walls ) Be careful with the projection screen it is fragile. Use the diode laser to measure the slit spacings for a couple of pairs of slits. Tape measures and rulers are provided. You may need to make L quite large, as these slits are pretty far apart. Try to keep the slide perpendicular to the incident beam otherwise our simple formulae need modification. 2

3 You may also want to try one of the Pasco double-slit slides. They may give cleaner results. PART 2 N-Slit Interference (1) Using either the appropriate column of the Cornell plate, or a Pasco slide, measure and compare the interference patterns for N = 2,3,4 (and 5 if possible) (2) Many-slit patterns: Observe the interference from the patterns in the central column of the Cornell plate. Measure the slit spacings for one of them. (3) Measure the interference pattern from the white United grating slide (300 lines/mm). These have many, closely spaced slits, and send laser spots all over the room. BE CAREFUL. (Do all our various small angle approximations still hold for these gratings?) PART 3 Diffraction (1) Observe the single-slit patterns from the Cornell plate or a Pasco slide. Measure one of them and compare to Eq. (4). The positions of the zeroes of intensity may be easiest to pick out. (2) Look at a multi-slit pattern. Can you see how the N-slit pattern is modulated by the single-slit diffraction effects? --- TO REPEAT: THIS IS A KEY FEATURE OF DIFFRACTION!! Spot spacing gives slit spacing, or in x-ray diffraction, the type of crystal lattice. Spot intensity is related to the width of each slit, or in x-ray diffraction, the set of atoms living at each unit cell of the lattice. PART 4 Extra Exercises Do these if you have time (and if we have equipment) (1) White light diffraction. Use the United grating or the Edmund grating to look at the spectrum an incandescent light (e.g. the flashlight). Explain what you see. Can you see n=1 and n=2? In diffraction grating language, the n=2 scattering is termed second-order. With the United grating you can see diffraction in both transmission and reflection. Can you see the wavelength dependence of the diffracted light? (2) White point-source diffraction. Look through your various gratings and the Cornell plate at the small white light bulb provided. You should be able to see all the interference and diffraction effects coming at you. (3) Other lasers: Observe (and perhaps measure) the wavelength of the light from a red laser. Compare to the green laser. 3

4 (4) Diffraction from a Compact Disk or DVD. A CD will give very nice white-light diffraction with a white light source. Try it with the overhead lamp. Even though the adjacent tracks on a CD or DVD are different in detail (they store different data), they are similar enough to diffract a laser beam. Reflect a laser off a CD and a DVD and try to observe the diffraction pattern. By comparing the two patterns, you should be able to tell whether the tracks are more closely spaced on the CD or on the DVD. Is this consistent with what you know about the data storage capacities of CDs and DVDs? If you have time, try to measure the track spacing. This works best if you turn the laser around, hold the CD against the Cornell plate at the end of the lab bench, shine the laser on the CD and look for diffraction spots back on the wall behind the laser. Question to ponder: A CD stores about 700 Megabytes of data. If you have measured the track spacing, you should be able to get a pretty good number for the linear bit density along the track. Remember that 1 byte = 8 bits.. 4

5 LAYOUT OF CORNELL PLATE 5