PHYS182B Lab 10 - Interference and Diffraction-1

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Dec 6, 2023

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PHYS 182B - Exp. 10 Interference and Diffraction Name Lab Partner Introduction: The distances between the central maximum and the diffraction minima for a single slit are measured by scanning the laser pattern with a light sensor and plotting light intensity versus distance. Also, the distance between interference maxima for two or more slits is measured. These measurements are compared to theoretical values. Differences and similarities between interference and diffraction patterns are examined, including the effect of changing the wavelength of the light. Single Slit Theory: When diffraction of light occurs as it passes through a slit, the angle to the minima (dark spot) in the diffraction pattern is given by a sin θ = mλ (m=1,2,3, …) (1) where "a" is the slit width, θ is the angle from the center of the pattern to a minimum, λ is the wavelength of the light, and m is the order (m = 1 for the first minimum, 2 for the second minimum, ...counting from the center out). In Figure 1, the laser light pattern is shown just below the computer intensity versus position graph. The angle theta is measured from the center of the single slit to the first minimum, so m equals one for the situation shown in the diagram. Notice that the central spot in the interference pattern is twice as wide as the other spots since m=0 is not a minimum. Since theta is a very small angle, sinθ ~ tanθ = x m /L, where x m is the distance from the center of central maximum to the m th minimum on either side of the central maximum and L is the distance from the slit to the screen. sin θ ≈ tan θ = x m /L (2) It is easier to measure the distance (Δx = 2x m ) from the m th minimum on one side to the m th minimum on the other side than to try to judge the center of the pattern. Equation (2) becomes sin θ ≈ tan θ = Δx /2L (3) Written by Ann Hanks and Alex Bates 1 Figure 1: Single Slit Diffraction
Our accuracy will be improved by making (Δx ) as large as possible. The slit width is not known very well. The uncertainty in the width is +/- 0.005 mm. That is a 25% uncertainty for the 0.020 mm slit. So instead of using the slit width to calculate a value for the laser wavelength, we use the known wavelength of the laser to calculate a more accurate value for the slit width. Procedure : - Turn on the Pasco Universal Interface and open Pasco Capstone in a computer - Open Hardware Setup to make sure the High Sensitivity Light Sensor and Rotary Motion Sensor are connected - In the Rotary Motion Sensor Settings (gear icon), make sure linear accessory is set to “rack and pinion” instead of “large pulley (groove)”: Written by Ann Hanks and Alex Bates 2
- The Red Diode Laser should be as far back at the end of the optics track as possible. Move the Diffraction Slit about 10 cm away from the laser. Make sure the light sensor setup is aligned parallel to the track. DO NOT STARE DIRECTLY INTO THE RED OR GREEN DIODE LASERS!! IT WILL DAMAGE YOUR EYES WHEN THE LASER IS NOT IN USE, TURN IT OFF AVOID AIMING IT AT YOUR CLASSMATES - Use the clear plastic pulley on the Rotary Sensor to slide the light sensor on the track side to side. With the sensor moved to the side, turn on the Red Diode Laser and make sure the laser is lined up correctly by aiming it at the wide, white plastic piece connected to the light sensor setup. If the laser is not aligned correctly, there are screws on the back of the diode laser to adjust its aim vertically or horizontally. You need to make sure the laser is properly ‘shooting’ through the diffraction slit as well as pointed at a proper spot so that the sensor can ‘see’ all of the light. Written by Ann Hanks and Alex Bates 3
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- Set the white Aperture Bracket disc (pictured above) to slot #5 with the 1.0 mm slit. Unlike the picture shows, make sure to set slot #5 in bottom so that the sensor device catches the light through the slot. - In Capstone, drag down a graph and for the y-axis, select the measurement Relative Intensity. For the x-axis, do NOT leave it on the default for Time, but instead choose Position. Position will be read from the Rotary Motion Sensor as you slide it along the gear-toothed track. - To start, you will use the Red diode laser and the 0.16 mm diffraction slit (one standing between the sensor and white disc). In Capstone you will measure the distance between the first and second minima. Then you will change to the 0.08 mm slit and measure those minima. You will then repeat that process for the Green Diode Laser. - Set the Common Sample Rate to 100 Hz at the bottom of the screen. - Click Record and start sliding the light sensor along the track by rotating the clear plastic wheel on the rotary sensor. It is best to have the light sensor start to one side or the other so that you only have to move it one way to gather data. - Note that your graph may default to meters for position, so you will have to zoom in on the horizontal axis to view the small millimeter movements you are making. - After you have finished taking data you should have a graph that depicts the various maxima and minima of the laser’s intensity. Use the Coordinate Delta Tool to measure the distance between the troughs of the first and second pair of minima: Written by Ann Hanks and Alex Bates 4
- The first and second minima correspond to m = 1 and m = 2 from the Theory section. Use the equations given to solve for the Theoretical distance between those minima and compare that to the distances you measured in Capstone (Experimental). Fill out the tables below with the various Measured and Calculated values and take the percent error. Written by Ann Hanks and Alex Bates 5
Red Laser, 650 nm Wavelength m = 1 Δ x Measured Δ x Calculated % Error 0.16 mm slit 0.08 mm slit m = 2 Δ x Measured Δ x Calculated % Error 0.16 mm slit 0.08 mm slit Green Laser, 515 nm Wavelength m = 1 Δ x Measured Δ x Calculated % Error 0.16 mm slit 0.08 mm slit m = 2 Δ x Measured Δ x Calculated % Error 0.16 mm slit 0.08 mm slit Written by Ann Hanks and Alex Bates 6
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