Physic 214 LaboratoryInterference and Diffraction
Interference of Light
Theory: Light that is incident upon two or more slits will interfere and produce an interference pattern on a distant screen. If coherent light with wavelength is incident upon two slits the light will interfere constructively and produce maxima on a distant screen when
d sin = m (see Figure 1) where d is the slit separation, m is an integer (m= 0, 1, 2, ...), and the angle is given by
tan = y/D
where y is the distance along the interference pattern, and D is the distance between the slits and the screen (see Figure 1). (Note, on your output, the intensity will be on the y-axis, and the distance y will be along the x-axis.)
In this lab we will study the interference of light that passes through two slits.
When light passes through a single slit, it is diffracted. The diffraction of light superimposes an envelope upon the pattern produced by the interference of light, as shown in Figure 2.
Figure 2. The expected constant peak for the intensity every time constructive interference occurs is modified by the single slit diffraction pattern to produce the pattern shown above. / Figure 1. a) A schematic of the arrangement for obtaining interference from a double slit showing the distances and other parameters needed for the equation of interference.
b) A schematic showing the path difference between ray 1 and ray 2. Note that D > d so the rays are nearly parallel.
Procedure and Calculations: Set up the laser light source, Multiple Slit Set wheel, screen, and light sensor as shown in Figure 3. In this experiment, we will study the interference patterns produced by 4 different double slits. These are labeled "Double Slits" on the "Multiple Slit Set" wheel.
Figure 3 The experimental apparatus with the multiple slit wheel in place.
The inputs to the Science workshop interface box are hidden by the label.
1). First, you need to set up Data Studio. Turn on the Science Workshop box, and then turn on the computer. Go to Start, Physics, Data Studio, and Create Experiment. Select Rotary Motion Sensor, and plug it into ports 1 and 2. Select Light Sensor, and plug it into port A. Click on the General, and change the frequency to 50 Hz. Click on the Rotary Motion Sensor tab and select 1440 in the Divisions/Rotation box. Click on Measurements, and select Position. Save these settings.
Click on the Light Sensor. Click on Measurements. Select Intensity. Save these settings by clicking OK. Click on the graph icon and drag in to Light Intensity. Click and drag the position icon to the X-axis of the graph, so you have a graph of Intensity versus position.
2). You need to make sure all of the equipment on the optical bench is set properly. Before turning on the laser and before placing the Multiple Slit Set wheelon the optical bench, set the slit width for the slit just in front of the light sensor to setting number 2. Set the gain on the Light Sensor to 100. Center the aperture apparatus on the linear translator and adjust the laser so it is incident in the middle of the slit in front of the Light Sensor. Do this using the two knobs on the back of the laser (only make adjustments using the knobs labeled "vertical" and "horizontal"). Place the Multiple Slit Set wheel on the optical bench close to the laser and adjust the slit wheel so the laser light is incident on the slit. If necessary adjust the laser again so the light strikes the center of the aperture slit. Select the first of the 4 double slits that you are going to study. Make sure that the interference pattern is bright and clear. If it is not, adjust the wheel so the pattern is bright and clear. The laser should only be on when it is necessary. Otherwise, turn it off. Do not look at the laser light directly.
3). Before you begin to record data, rotate the wheel around to see the different types of interference and diffraction patterns produced by the different slit sets on the wheel.
4). You are ready to record data. Start with the intensity pattern off to the side on the white screen. Set the wheel on the first of the four double slit sets you are going to study. Press the Start button. Very slowly, move the wheel behind the Light Sensor to move the interference pattern across the Light Sensor. When you are done, press the Stop button.
5). Click on "Scale to Fit," which is the icon on the graph in the upper left hand corner. You should see the intensity pattern inside the envelope of the diffraction pattern.
6). Use the "Smart Tool" (which is the icon that looks like a coordinate graph) to accurately record the coordinates of several of the maxima and minima of the pattern. [To be able to completely control the Smart Tool, double click on the graph, then click on the Tools tab and find the Gravity setting on the upper left. Set the Gravity to “0”. Click OK until you exit the window(s)] Print out the graph.
7). Record the wavelength of the light, and the distance between the slit and the screen.
8). Use your observations to determine the separation between the two slits. Compare this with that printed on the Multiple Slit Set wheel. Discuss the intensity pattern, and the diffraction pattern. How does the slit width, a, affect the envelope around the intensity pattern?
9). Repeat these steps for the other three combinations of slit width and slit separation until you have studied all four combinations on the wheel.
Diffraction of Light
Theory: Light that is incident upon a more slit will be diffracted and produce a diffraction pattern on a distant screen. If light with wavelength is incident upon a slit of width a, the light will interfere with itself destructively and produce a series of maxima and minima on a distant screen; minima are produced whena sin = m
(see Figure 4) where m is an integer (m= 1, 2, ...), and the angle is given by
tan = y/D
where D is the distance between the slit and the screen, and y is the distance along the diffraction pattern (see Figure 4). (Note, in the plots you will produce for this lab, the intensity will be on the y-axis, and the distance along the diffraction pattern, y, will be on the x-axis.)
In this lab we will study the diffraction of light that passes through slits with different properties.
Figure 5 The relative intensity pattern for single slit diffraction. /
Figure 4 Diagram of the light path (a) and path difference (b) for a single slit diffraction pattern
Procedure and Calculations:
1). Remove the Multiple Slit Set wheel, and adjust the laser so it is incident in the middle of the slit in front of the Light Sensor, if necessary. Do this using the two knobs on the back of the laser (only make adjustments using the knobs labeled "vertical" and "horizontal"). Replace the Multiple Slit Set wheel with the Diffraction Set wheel. The Data Studio settings are unchanged from the previous experiment.
2). Before turning on the laser, check the settings for the the slit width for the slit just in front of the light sensor. It should be set to setting number3. Be sure the gain on the Light Sensor is set to 100. Select the first of the single slits that you are going to study. Make sure that the diffraction pattern is bright and clear on the white screen. If it is not, adjust the wheel so the pattern is bright and clear. The laser should only be on when it is necessary. Otherwise, turn it off. Do not look at the laser light directly.
3). Before you begin to record data, rotate the wheel around to see the different types of interference and diffraction patterns produced by the different slit sets on the wheel. First, we will study the diffraction pattern of the 4 single slits on the wheel.
4). You are ready to record data. Set the wheel on the first of the four double slit sets you are going to study. Press the Start button. Very slowly, move the wheel behind the Light Sensor to move the diffraction pattern across the Light Sensor. When you are done, press the Stop button.
5). Click on "Scale to Fit," which is the icon on the graph in the upper left hand corner. You should see the intensity pattern of the diffraction pattern.
6). Use the "Smart Tool" (which is the icon that looks like a coordinate graph) to accurately record the coordinates of the minima of the pattern. Print out the graph.
7). Record the wavelength of the light, the distance between the slit and the screen, andthe width of the slit printed on the Diffraction Set wheel.
8). Repeat these steps for the three other slit widths until you have studied all 4 single slits on the wheel.
9). Use your observations to determine the width of each slit. For each slit, compare your experimentally determined width with that printed on the Single Slit Set wheel. Discuss how the slit width a affects diffraction pattern.
10). Study the diffraction patterns of the square, hexagonal, random opaque dot, random hole, opaque line and circular aperture patterns.
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