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the questions are number 2 and 3 on the second pic and question 2 on the 3rd pic
Objectives 1. Introduce diffraction, interference, and the wave nature of light 2. Determine and compare the wavelength (color) of the laser using single- and double-slit experiments (lab report) Materials & Resources 1. Single and Multiple diffraction slit wheels, Red diode laser (650.0 nm), Optics track with three adapters 2. Aperture bracket, Rotary motion sensor, High sensitivity light sensor, Linear translator, Interface box with Capstone Introduction Under certain conditions, light behaves like photons or particles of light traveling through space in straight lines. This happens when the surface or aperture that the light interacts with is very large compared to the wavelength of the light The previous labs involving the laws of reflection and refraction, which led to the thin lens equation and geometrical optics, are based on the condition that the lenses and other surfaces and apertures are all large compared to the wavelength of visible light, which is between about 400 - 700 nm. But when this condition is not met and when the size of the surface or aperture interacting with the light is about the same size as the wavelength of the light involved, the light behaves like other waves (sound, water, etc.). As such, under the right conditions, light will undergo diffraction and interference just the same as other waves. Diffraction is when a wave (of any sort) bends around an obstruction in its path. Diffraction of sound waves is the reason you can hear someone shout around a corner. Interference is when more than one wave obey the principle of superposition at a particular point in space, that is, the amplitudes of each wave adds to form the amplitude to the resultant wave. Think about throwing two rocks into a lake some distance apart but at the same time. The reason the waves that form in between where the rocks land in the lake is larger than the waves outside this region is because the waves generated by each rock add together in the middle. When two waves of the same amplitude and frequency are in phase the resultant wave has twice the amplitude and the same frequency of the original waves. When they are 180ºor n out of phase, the amplitude becomes zero for the resultant wave. This is called constructive and destructive interference, respectively. Now, to ensure that the waves that strike a single double, or multiple slit are of the same amplitude and frequency, we can use the light from a monochromatic (only one frequency or color) source a long way away or a laser beam, which closely approximates a monochromatic plane wave across the beam profile. So we will use a red diode laser in a single-slit and a double-slit experiment to determine the wavelength of the laser light. The formulas for this are as follows: For a single slit, mi-a sin @ where m is an integer that counts the dark spots from the center on each side of the center maximum, à is the wavelength of the laser light, a is the width of the single slit, and 0 - arctan (). *D), where y. is the distance from the center of the interference pattern to the dark spot and L is the distance from the slit to the screen. For a double slit, nid sin , where n is an integer that counts the bright spots from the center of the interference pattern on the screen, à is the wavelength, d is the separation between the centers of the two slits, and e-arctan (y.+), where yn is the distance from the center of the interference pattern to the bright spot and L is the distance to the screen. Note how similar these two equations are. The main difference is that m counts the dark spots for the single slit interference pattern whilc n counts the bright spots of the double slit pattem. Also, a is the width of the single slit and d is the separation between the centers of the two slits in the double slit experiment. a
0.754 10.00066 in adamlar 6x 104, z. 9x107 > 5 10.0075 0.0075 0.0075 16) Enter your calculated values for the laser wavelength into a new empty data table in Capstone, find the average and standard deviation of the double slit experiment and record these results to the right 17) Calculate the percent error in your experimental results using the accepted value of 6.500x10 m and record to the right Show your work below % Error in in 99 Questions 1) Is your experimental value for the laser wavelength higher or lower (circle one) than the accepted value? 2) What does this result say about your measured value for L, assuming your measurements for the y. were perfect? Clearly justify your answer below. 3) What does this result say about your measured values for y., assuming your measurement for L. was perfect? Clearly justify your answer below. 4) Is your % error in áo greater or less (circle one) than your standard deviation din? What does this imply about the validiny of determining the wavelength of a laser using the experimental method above? Justify your answer below. That one experiment is invalid. To error should be so or less.
2) How do the graphs patterns for double and single slit look similar? How do the patterns look different?
DOUBLE SLITS 0.00 0.50 0.00 o.se SCOP 10'S 100** VARIABLE DOUBLE SLIT 2010 0.75 다 2004 1. Determination of Wavelength of Light with Double Slit Experiment (Lab Report) Background Multiple Slits Wheel The Pasco High Precision Diffraction Slits are used in this lab. The multiple slit wheel contains several groups of slits with different numbers of slits and spacings (Pasco labels slit width as a and slit separation as ) VERY IMPORTANT WARNINGS!!! Do not leave the laser on when you are not using it! ID: Do nor look into the laser this can be very dangerous! HIGH PRECISION Remove all jewelry now (rings, bracelets, or watches) DIFFRACTION SLITS Do not proceed any further until these items are gone! MULTIPLE Procedure SLITS 1) Rotate the wheel of double slits until the 40,04 mm and d-0.25 mm double slit is set to the 9 o'clock position 2) Mount the laser on the end of the opties bench (may need dynamics track adapter). Mount the High Precision Double Slit disk to the optics bench with the printed side toward the laser as shown (see Figure 2) Turn on the laser and make sure your selected double slit is being hit by the laser 3) Step 3 should already be done before you arrive at lab, but incase it isn't, mount the Rotary Motion Sensor on the rack of the Linear Translator and mount the Linear Translator to the end of the optics track (see Figure 3). Arrange things so the black stop block on the linear translator arm is on the left side as viewed from the laser and all the way against the bracket. Mount the Light Sensor to the Aperture Bracket (set on slit #6) with the 3 cm black rod. Mount the black rod in the Rotary Figure 2 (Courtesy of Pasco) Motion Sensor rod clamp. The Light Sensor should be aligned with the bracket soit points parallel to the optics track 4) Move the light sensor until you can see the beam somewhere on the white screen of the aperture. Use the adjustment screws on the back of the laser to adjust the position of the laser beam from left-to-right and up-and-down to make the patter on the white screen as bright as possible and at the correct height of the light sensor (see Figure 4). Once this position is set, it is not necessary to make any further adjustments of the laser beam when viewing any of the slits on the disk. When you rotate the disk to a new slit, the laser beam will be already aligned. Since the slits click into place, you can easily change from one slit to the next even in the dark MULTIPLE SLITS SNOSIUVINO Figure 3 (Courtesy of Pasco)
15) For each row in the table, calculate the average distance yes, the angle and the wavelength is using the formulus given in the first row of the table, 0.25 71 0.003 0.003 0.00064 4 Left Right Average Angle Wavelength Yol w V-+2 0.tan) 2.- (d sinn 1 0.6015 10.0615 0.0015 0.151 0.0006 2 0.003 0.302 0.0001 3 10.0044 0.0040 0.0045 0.44 0.ool 0.00 0.bou 0.603 0.00066 S 10.0075 0.0075 0.754 0.00066 16) Enter your calculated values for the laser wavelength into is = dio-656X10" 7.9 X10 a new empty data table in Capstone, find the average and Standard deviation of the double slit experiment and record these results to the right 17) Calculate the percent error in your experimental results using the accepted value of 6.500x16m and record to the right 4. Emorino Show your work helow. 10.0075 Questions: 1) Is your experimental value for the laser wavelength higher or lower circle one) than the accepted value? 2) What does this result say about your measured value for Lassuming your measurements for the y. were perfect? Clearly justify your answer below. 3) What does this result say about your measured values for y., assuming your measurement for L was perfect? Clearly justify your answer below. 4) Is your % error in a greater or less (circle one) than your standard deviation dåp? What does this imply about the validity of determining the wavelength of a laser using the experimental method above? Justify your answer below. That one experiment is invalid. on enor should be solo or less.
5) Plug the Rotary Motion Sensor and the Light Sensor into the PASPORT inputs on the Interface box. Open Capstone and click open the Hardware Setup button at the left of the screen. Click on the Rotary Motion Sensor icon. To the right of where it says Rotary Motion Sensor at the bottom of the Hardware Setup panel, click on the Gear icon. In the Linear accessory line, click on the white triangle and select Rack & Pinion Click OK Click the Hardware Setup button to close the screen Figure (Cartesy of 6) in Capstone, set the Common Sensor Sample Rate 10 100 Hz. Create a graph of Relative Intensity vs. Position 7) There are three buttons on the Light Sensor to set the sensitivity. For maximum sensitivity, press the (0-1) button. If the Light Intensity goes too high (it will flatline at 100% on the graph, turn the sensitivity down by pressing the (0- 100) button on the Light sensor if you reach 100% intensity at any time on the graph You'll use the (0-100) button for both the double slit and single slit experiment. Press the (0-100) button now 8) Move the Light Sensor so the Rotary Motion Sensor (RMS) is against the black stop block on the linear translator arm 5 3 9) Click Record and slowly turn the RMS pulley to scan the patter. Hold the rear of the RMS down against the linear translator bracket so it does not wobble up and down as it moves. Click on STOP when you have finished the scan. I the intensity makes out (100%), change the gain setting on the light sensor and repeat the run 10) Click on the Scale-to-Fit button double-click on a maxima and select the Coordinate Tool Right click in the center of the display that appears and select Tool Properties. Under Numerical Format, increase the number of significant figures to 4. We actually want 4 decimal places which means significant figures when the positions are greater than 0.1 meters 11) Locate the central max yv (n-0). Double-click on the maxima and select the Coordinate Tools Record the distance with correct significant figures and units below. 1.-0.610 m) 12) Locate the left and right max for n-1. The table for data refers to the left max for n-1 as yn and the right max for 1 asy. For each value of n yu and you represent the left and right distance from the central max y Double click on the maxima of the left nmax and select the Coordinate Tool. We want to record the distance from the central max, so take the absolute difference of the max's position and there is also a Delta tool that will get the distance without having to subtract values which is easier). Record the distance value in the table as yw for with correct significant figures and units. Do the same Figures for the right max for 1. 13) Repeat step 12) and record the values for yw and yw for -2.3.4, and in the table with correct significant figures and units. Label the graph now or after printing and print a graph of the Relative Intensity vs. Position for each lab member 14) Use the built-in ruler of the optics track to measure the distance between the double slits and the screen: Record the distance with correct significant figures and units, Figure -rom)
0.16 0.00 SINGLE SLITS VARIABLE SLIT ** 20.20 8.25 2. Determination of Wavelength of Light with Single Slit Experiment Procedure: 1) Turn the laser off if you haven't already. Replace the Single Slits Wheel double slit Pasco wheel with the single slit Pasco wheel 2) Rotate the wheel of single slits to the a-0.08 mm slitas shown in Figure 7. Position it at 9 o'clock. 3) Use the adjustment screws on the back of the laser to adjust the position of the laser beam from left-to-right and up-and-down to make sure the patter on the white s screen is still bright as possible, HIGH PRECISION 4) Move the Light Sensor so the Rotary Motion Sensor DIFFRACTION SLITS (RMS) is against the black stop block on the linear translator arm. SINGLE 5) Click Record and slowly turn the RMS pulley to scan the SLITS patter. Hold the rear of the RMS down against the linear translator bracket so it does not wobble up and down as it moves. Click on STOP when you have finished the scan. If the intensity makes out (100%), change the gain setting on the light sensor and repeat the run. If the intensity is too weak, press the higher Figure 7(Courtesy of Pasco) sensitivity button 6) Locate the central max y* (n=0). Double-click on the maxima and select the Coordinate Tool; Record the distance with correct significant figures and units to the right -0.012 ) 7) Complete the table below except now measure to the center of all 4 dark areas on the left and right sides of the central maximum. Label the graph now or after printing, and print a graph of the Relative Intensity vs. Position for cach lab member CIRCULAR APERTURES 3 SAARE NE 200 אסון 100 un/a SENPLAVA 8) Use the built-in ruler of the optics track to measure the distance between the double slits and the screen; Record the distance L with correct significant figures and units to the right. L-67 9) For each row in the table, calculate the average distance me the angle and the wavelength ham using the formulas given in the first row of the table. 77 1 10.0032 0.0009 2 Left Right Average Angle Wavelength 'M me-0/+ y)2 -tanl/) m = (a sinn/m 10.0225 0.0064 0.01445 2.26 10.0862 0.0093 0.00775 0.62 10.0107 10.0113 0.04185 1.08 0.0015 10.0153 0.0134 0.01435 6.0021 0.0191 0.0151 0.0171 1.92 0.0027 3 4 1.54 5
10) Enter your calculated values for the laser wavelength into a new emply data table in Capstone, find the standard deviation of the single slit experiment and record these results to the right 11) Calculate the percent error in your experimental results using the accepted value of 6.500x10 m and record to the right Show your work below is dis -0.00208 +0.000918 99 Error in s Central 1 Screen left right Singlese Laser Figure 8 Figure Questions: 1) Based on your values for error and standard deviation for both the single and double slit experiments, which method is better for determining the wavelength of a laser? Justify your answer. neighther they both gave the same amount of solenor. 2) How do the graphs patterns for double and single slit look similar? How do the patterns look different?