Diffraction lab

Single Slit Diffraction INTRODUCTION As long ago as the 17th century, there were two competing models to describe the nature of light. Isaac Newton believed that light was composed of particles, whereas Christopher Huygens viewed light as a series of waves. Both models could explain reflection and refraction, but the phenomena of diffraction and interference could be more easily explained by Huygens’ wave model. In the early 19th century, Thomas Young’s double-slit experiment provided evidence that supported the wave nature of light. This is the first of two experiments that examine the phenomena of diffraction and interference, which occur with all types of waves from water to light. Diffraction is the spreading of light when it passes an edge or through an aperture. The amount of spreading depends upon the wavelength of the light and the width of the aperture. At the screen, photons interfere with themselves due to the path length differences of the possible paths the photons can take as they pass through the aperture and reach the screen. This causes an interference pattern to be formed on the screen. OBJECTIVES In this experiment, you will • • • Measure the features of the pattern produced on a screen when light from a laser passes through one slit. Use theory to predict where destructive interference will occur in the single slit diffraction pattern. Compute the degree to which theory matches your observational measurements. MATERIALS Vernier data-collection interface Vernier Graphical Analysis app Diffraction Apparatus ruler Vernier Optics Expansion Kit Vernier Dynamics Track Green Diffraction Laser (optional) INITIAL INVESTIGATION DO NOT LOOK INTO THE LASER!! Direct exposure of the eye by a beam of laser light should always be avoided with any laser, no matter how low the power. 1. Attach the laser at one end of the track so it faces down its length. Connect the power supply. Leave the laser off until all parts are in place to avoid accidental reflections. 2. Set the diffraction slit assembly to a single slit of width, a = 0.08 mm. Attach the assembly to the track, with the silver reflective side of the glass plates facing the laser. Position it about 10 cm from the laser assembly. 3. Attach the High Sensitivity Light Sensor and the Linear Position Sensor to the opposite end of the track, with the light sensor facing the slits. The more space between the sensor and the diffraction assembly, the greater the spacing in the interference pattern, so maximize this to diminish the effect of ruler measurement errors. 4. In the data table, record the distance, D, from the slit assembly to the light sensor. Keep this distance fixed throughout the experiment. 5. Record the wavelength, , of the laser in the data table. Figure 1 Laser and slit assembly Figure 2 Light sensor assembly 6. Turn on the laser. Adjust the horizontal laser position to achieve maximum brightness of the pattern. Adjust the vertical laser position to center the pattern vertically on the entrance aperture of the light sensor. Use this procedure every time you change the slits. 7. Slide the light sensor assembly so that the pattern from the beam falls on the screen to one side or the other of the aperture disk (see Figure 2). Draw or describe the features of the single slit pattern below. MEASUREMENT OF THE SINGLE SLIT PATTERN TRIAL 1: 1. Make sure the diffraction slit assembly is set to a single slit of width, a = 0.08 mm. Record the slit width, a, in the data table. 2. Turn on the laser. Adjust the laser position if necessary. 3. Using a ruler, measure and record the distance between the centers of the first dark fringes. Repeat this measurement for the second dark fringes, and for the third dark fringes if they are visible. Record these measurements in the data table. 4. Divide these width values in half to give you the distance from the center of the pattern to each dark spot. Record these values in the data table. 5. Connect the High Sensitivity Light Sensor and the Linear Position Sensor to the interface and start the data-collection program. 6. The optimal combination of light sensor sensitivity and sensor aperture depends on the type of laser and the slit configuration. It allows an intensity reading that reveals the detail necessary for you to make your measurements. For the red laser and the single-slit configuration you used in Part 1, we suggest setting the sensitivity to 1 W and using an aperture of 0.5 mm. 7. Move the sensor assembly all the way to one side of the sensor track (i.e., move it perpendicular to the main laser track). Zero both sensors. 8. Start data collection, and then slowly slide the sensor assembly stage toward the other side of the sensor track on which it is mounted. You will be moving the sensor across the interference pattern (like a scan of it). Take at least 20 seconds to execute the motion, slowing when the sensor is traversing the brightest portions of the pattern. Stop collecting data when the stage reaches the end stop. Test that you moved the stage sufficiently smoothly by storing the run and collecting another run, moving the stage in the opposite direction. The trace of the second run should overlay that of the first. 9. In Graphical Analysis, view the intensity vs. position graph for your first slit width measurements. Zoom in on the portion of the graph that shows the first three dark spots on both sides of the central maximum. Choose the Examine tool from the Analysis menu and position the cursor on the peak corresponding to the central maximum. Record the position of the central peak in the data table. Record the positions of the first three bright fringes on either side. If it is difficult to find the third bright fringe, explain why. 10. Determine the distance, yn, from the central maximum to the first three bright fringes on either side. If the distances are not the same on either side, decide how to best report them (i.e., use the average). Record these distances from the central peak to each of the first three dark fringes in the data table. TRIAL 2: 11. Choose a different single-slit configuration in which you change the slit width, then repeat the previous steps for the new slit width. You may find it necessary to change the aperture on the light sensor to obtain sufficient detail to complete your evaluation of data. When you are finished collecting data, save your experiment file and turn off the laser. TRIAL 1 Wavelength (nm) D, distance to screen (cm) a, slit width (mm) Ruler Dark Fringe Distance between dark fringes (cm) Ym Distance / 2 (cm) Graphical analysis Measured Ym position measured (cm) distance (cm) Desmos Ym theoretical distance (cm) Graphical analysis Measured Ym position measured (cm) distance (cm) Desmos Ym theoretical distance (cm) Percent Error (Graphical Analysis vs Theory) Single slit – m = 1 Single slit – m = 2 Single slit – m = 3 TRIAL 2 Wavelength (nm) D, distance to screen (cm) a, slit width (mm) Ruler Dark Fringe Distance between dark fringes (cm) Ym Distance / 2 (cm) Percent Error (Graphical Analysis vs Theory) Single slit – m = 1 Single slit – m = 2 Single slit – m = 3 THEORETICAL PREDICTIONS 1. Read the materials in the Appendix at the end of the lab. 2. Identify the formula for single slit diffraction that gives the light intensity on the screen as a function of distance from the center of the pattern, slit width, and distance from the slits to the screen. Write the formula below. 3. Make a model of this formula in Desmos where y represents the intensity on the screen and x represents the distance from the center of the pattern (i.e., the center sits at x=0). You will need to add sliders for slit width, a, and distance from the slits to the screen, D. 4. Make sure the Desmos model generates an intensity vs distance graph is like the diffraction patterns that you observed. 5. In your Desmos model, for each trial, use the value for your slit width as the value for a, and the distance from the slits to the screen as your value for D. Then find the predicted distances of the first three minima (i.e., the x-values where the y value representing intensity goes to zero, the first three places where the curve touches the x-axis). Record these values in the theoretical columns of the respective data tables for trials 1 and 2. 6. Save your Desmos model and paste a hyperlink to it below. EVALUATION OF DATA 1. How does the single-slit pattern change as you change the slit width? Test your prediction if necessary. 2. Compute the percent error between the theoretical values of the distances to the first three dark fringes and the distances you measured with the Vernier light sensor. Record those values in the respective data tables for trials 1 and 2. 3. Compare your findings with those of other groups. How do your percent errors compare to other groups? If your errors are comparatively high, explain the potential causes of why your error is higher than other groups. 4. Describe the phenomenon of diffraction in your own words. 5. Describe the phenomenon of interference in your own words. 6. What did you learn from completing this lab? APPENDIX The single slit pattern is given by 𝜋𝑎𝜃 2 𝜆 ) 𝐼 = 𝐼0 ( 𝜋𝑎𝜃 𝜆 sin where a is the slit width. Recall the small angle approximation, 𝜃 ≈ 𝑦/𝐷, where y = distance from central maximum on screen, and D = distance from slit to screen. Under the small angle approximation, our intensity pattern becomes 𝜋𝑎𝜃 2 sin 𝐷𝜆 ) 𝐼 = 𝐼0 ( 𝜋𝑎𝑦 𝐷𝜆 The zeros for the intensity (dark spots) occur when the sine function equals zero. The sine function 𝜋𝑎𝑦 equals zero when 𝐷𝜆 = 𝑛𝜋 where 𝑛 = 1, 2, 3 … Therefore, we have 𝑎𝑦 =𝑛 𝐷𝜆 Solving for y, we have for the location of the zeros 𝑦= 𝑛𝜆𝐷 𝑎

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