PHYS320(O) ilab Experiment 4 Instructions Diffraction and Interference: Measurement of the Wavelength of Light

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1 Objective: PHYS320(O) ilab Experiment 4 Instructions Diffraction and Interference: Measurement of the Wavelength of Light The purpose of this activity is to determine the wavelength of the light emitted by a diode laser and LEDs (light emitting diodes). Parts and Equipment Required: Laser pointer Binder clip Grating or lens stand Diffraction gratings (500 lines per mm and 1000 lines per mm) 5 3 by 5 (or larger) index cards Kit box, lid, or other large white surface Solderless breadboard Red, yellow, green, and blue LEDs 220 ohm resistor 9 V battery and battery clip Electrical tape Hobby knife or other sharp knife Ruler marked in centimeters or vernier caliper Introduction: A transmission grating is a piece of material that has a pattern of a large number of equally spaced lines or grooves. When monochromatic light shines on the grating, each groove diffracts the light, and each wave front interferes with the wave fronts from all the other grooves (see Figure 1). PHYS320 ilab (O) Instructions Page 1 Experiment 4

2 Figure 1 Diagram of diffraction grating showing wave fronts and direction of beam travel. Each light wave will be in phase when it arrives at a point at an angle θ m, such that: dsinθ m = mλ, where d is the grating spacing, λ is the wavelength of the light, and m is an integer that denotes the order of the fringe. The result is a distinct interference pattern that can be projected on a screen, as shown in Figure 2. Figure 2 Diagram of diffraction experiment showing position of interference fringes PHYS320 ilab (O) Instructions Page 2 Experiment 4

3 If the line spacing is known, then measurements of the distance between orders and the central maximum can be used to calculate the wavelength of the light. Predictions: How does the diffraction pattern change as the distance between the laser and the diffraction grating changes? How does the pattern change as the distance between the grating and the projection screen changes? Procedure: I. Part 1: Set-up 1. Set up for this experiment as shown in Figure 3. Figure 3 Set-up for Part 1 of Lab 4 2. Elevate the laser pointer using a binder clip as a stand. You might need to use a book or pad of paper to adjust the height of the laser. Place the 1000 lines/mm diffraction grating in a grating stand. 3. Position the kit box on the opposite side of the grating as the laser, cm from the grating. You will use this as a screen to mark the position of diffraction maxima. NOTE: You may also affix a piece of paper to the box surface for easy removal and measurement. WARNING: DO NOT LOOK DIRECTLY INTO THE LASER! 4. Adjust the position of the binder clip so that the laser is on. Shine the laser light through the diffraction grating and on to the kit box. You should see a central bright spot of light and two dimmer spots to the left and right of the central spot. The spots to the left and right of the central spot are the first order interference maxima. You might see additional dimmer spots spaced further away. These are the second order interference maxima. Vary the distance between the grating and the screen and the distance between the laser and the grating. Record your observations on the data sheet. PHYS320 ilab (O) Instructions Page 3 Experiment 4

4 II. Part 1: Data Collection 5. Set the grating a convenient distance between 10 and 20 cm from the screen. Carefully measure the screen-grating distance and record it as L on your datasheet. You may wish to tape the grating stand to the table surface so that it does not move. 6. Mark the locations of the central spot and the two first order spots with a small x on the screen. Carefully measure the distance between the left first order spot and the central spot. Then measure the distance between the right first order spot and the central spot. Record these distances as y in the table on your data sheet. 7. Repeat for the 500 lines/mm grating. III. Part 1: Analysis 8. Calculate the diffraction angle θ for each measurement by using the formula: θ = tan 1 y L 9. Use the data from the red laser to compute the laser wavelength for each measurement with the formula: λ = d sin(θ) where d is the grating spacing. The grating spacing for each grating is the reciprocal of the number of lines per mm. Calculate the average wavelength. Record the known wavelength of the laser and calculate the percent discrepancy of your measurement. IV. Part 2: Set-up 1. Use a hobby knife or some other sharp blade to carefully cut an approximately 1 mm by 20 mm slit in the center of an index card. Use electrical tape to cover (except for the slit) one side of the card to stiffen the card and to block light. The final result should look similar to Figure 4. Figure 4 Index card with 1mm by 20 mm slit covered with electrical tape 2. Insert the card into the same grating stand as the 500 lines/mm diffraction grating and set it aside. PHYS320 ilab (O) Instructions Page 4 Experiment 4

5 3. Use the solderless breadboard, a 220 ohm resistor, a red LED, the 9V battery, 9V battery clip, and a short piece of hook-up wire (optional) to build the circuit shown in Figure 5. Figure 5 LED circuit diagram 220 Ω 9V LED 4. LEDs conduct current in only one direction. Be sure that the shorter lead (flat side of the plastic case) is connected to the negative (minus) terminal of the battery. Photographs of the completed circuit are shown in Figures 6 and 7. Figure 6 LED circuit on breadboard PHYS320 ilab (O) Instructions Page 5 Experiment 4

6 Figure 7 LED circuit with battery You may wish to use the binder clip as a stand to hold the breadboard vertically. Make sure that the LED lights up when the battery is connected. 5. Insert an index card into a grating stand to use as a screen. Stand the breadboard vertically and set the stand with the slit and grating between the breadboard and screen. Adjust the position of the circuit so that the light from the LED shines through the slit and onto the screen. The set-up is shown in Figure 8. Figure 8 Set-up for Part 2 of Lab 4 6. The first order interference maxima will be very dim. You will need to set up this experiment in a room that can be made as dark as possible. If too much light comes in through a window, you might have to wait until night to complete this part of the experiment. PHYS320 ilab (O) Instructions Page 6 Experiment 4

7 7. Adjust the distance between the screen and the grating until the first order fringes for the red LED are just at the edges of the index card screen. Tape the grating stand and the stand with the screen to the table so that they cannot move. Carefully measure the distance between the screen and grating. Record this distance as L on your datasheet. 8. Mark the center position of the central, left, and right fringes with a pencil. Remove the index card and carefully measure the distance between the left fringe and the central fringe and between the right fringe and the central fringe. Record these distances as y in the table for the red LED. 9. Replace the red LED with the yellow, green, and blue LEDs in turn and repeat the procedure. 10. (Optional) Try using the amber and white LEDs. Observe the result. V. Part 2: Analysis 11. Calculate the diffraction angle θ for each measurement by using the formula: θ = tan 1 y L 12. Use the data to calculate wavelength for each LED with the formula: λ = d sin(θ) where d is the grating spacing. The grating spacing for each grating is the reciprocal of the number of lines per mm. Calculate the average wavelength for each LED. 13. Complete the data sheet and turn it in to your instructor. PHYS320 ilab (O) Instructions Page 7 Experiment 4

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