Double Slit Interference

Transcription

1 Introduction Double Slit Interference The study of interference and diffraction of light is a keystone to the understanding the behaviour of light. This experiment begins to look at the wave-particle duality of light. The study of diffraction of light through a single slit and intereference and diffraction of light through double slits is a simple experiment that laid the groundwork for modern physics. In the single slit experiment, diffraction pattern as a function of slit width is studied. In the double slit experiment, both slit width and slit separation is considered. This lab uses laser diodes that do not require additional eye protection when using them. However, it is highly recommended to avoid exposing or staring at the beams for prolonged durations. The lab tries to minimize this by taking measurements on paper after marking the light patterns observed. The lab will be run in a dark(ened) room to better enhance the patterns observed. Desk lamps are provided in the event you need some light. A low resolution version of the optical equipment Apparatus Optics Rail Laser Diode λ = 650 nm, <1 mw output Multiple Slit Accessory Single Slit Accessory Desk lamp 9 V 500 ma AC adaptor Viewing Screen /w magnets (2) Calipers Paper Pre-Lab Questions Please complete the following questions prior to coming to lab. At the beginning of lab, you will be given a short quiz which is heavily based on one (or more) of these questions. Page 1 of 6

2 1.) Read through the entire lab writeup before beginning. Ryerson University - PCS ) Briefly explain the difference between white light and monochromatic light? 3.) What is coherence of light and its importance to the lab? 4.) Can two distinct sources produce an observable interference pattern? 5.) Can two monochromatic sources of significant frequency difference produce an observable interference pattern? 6.) In a double slit experiment, the distance between the two slits, d, is 0.5 mm and the wavelength of the light used is λ = 690 nm. What is the distance on the viewing screen between the central maximum (m = 0) and the second order maximum (m = 2) when the screen is placed 1 m away from the slits. Part I - Single Slit Diffraction As light passes through a single narrow slit of width a, a diffraction pattern is be observed. A classical analogy is observing water waves through a narrow opening. The interference of the waves creates minima in specific locations that follow the equation: a sin θ = mλ; m = 1, 2, 3,... (1) Here, θ is the angle from the centre line and m is the minima order number which counts outward from either side of the central maxima. Single Slit Diffraction Pattern If we were to measure θ directly, it would be quite difficult so a few tricks are employed. First, it s noted that the distance from central maxima to minima y m is (or should be) much smaller than the distance between the single slit and screen, D. Thus using some trigonometry, small angle approximation, and rearranging, we obtain the following result: y single,m = mλd a ; y D (2) Page 2 of 6

3 Procedure I Ryerson University - PCS ) Set up the laser diode on one end of the optics rail, viewing screen on the opposite end, and single slit disk approximately 3 cm in front of the laser as shown above. 2.) Adjustments to the horizontal and vertical position of the laser beam is achieved by using the correspondingly labelled thumb screws on the back. Do not over tighten or over loosen these screws - the alignment should be within the operating range. 3.) On the single slit disk, rotate the disk such that the laser properly intersects the Variable Slit portion of the disk. A single slit diffraction pattern should be observed on the viewing screen. 4.) Rotate through the variable slit region and observe how the diffraction pattern changes as you adjust the slit size. Comment on what you observe (and include it in your final report). 5.) Measure the distance between the slit to viewing screen, D single. Note that the slit is actually offset from the indicator line of the slit holder and must be taken into account. 6.) Rotate the disk to the Single Slit portion and select a slit width, a of 0.02 mm ensuring a pattern forms on the viewing screen by adjusting the thumb screws as necessary. 7.) Attach a piece of paper with a straight line drawn on it to the viewing screen and adjust it such that the line is in alignment with the diffraction pattern. To the best of your ability, mark the minima on either side of the central maxima along the line. Label the pattern on the paper accordingly for your own recordkeeping. 8.) With calipers, measure the distance between the two first order minima (m = 1) as well as the distance between the two second order minima (m = 2) if possible. Record these values as 2y m along with a reasonable uncertainty. 9.) Repeat this process for all other slit widths, a = 0.04 mm, 0.08 mm, 0.16 mm. For the analysis to work, slit to screen distance D should not change - it might be wise to check all the configurations first before recording data to ensure that you can get good measurements. Analysis I 1.) Determine the distance from the central maxima y single,m by halving the measured distances between minima. 1 2.) On a single graph, plot inverse slit width,, versus distance from central maxima, a y single,m, for both order of minima. Page 3 of 6

4 3.) Apply a linear fit to both the data sets and comment on how their slopes compare to one another. What was expected? 4.) From the plot, make a statement about how slit width and the distance between minima are related. 5.) Do you expect the lines to intersect? If so, where should they and how would you describe the physical configuration, and what you would see. 6.) Rotate back to the variable slit region and set it to an arbitrary slit width. Using the procedure above and the plot you made, determine the slit width you had set. Part II - Double Slit Interference Next, we consider the effect of light as it passes through two slits of width, a, and separation d. In this case, an interference and diffraction pattern are observed. The interference pattern arises from two coherent sources creating constructive and destructive interference with one another. The classical analogy is listening to two speakers (playing the same thing) separated some distance away from one another. In this case, since light is still travelling through single slits (two of them), single slit diffraction is also observed. Since both are occuring at the same time, the two shapes are multiplicative and one observes the interference pattern encapsulated by a diffraction pattern. The minima due to interference is given by the following condition: d sin θ = mλ; m = 1, 2, 3,... (3) Using the same approximations as the single slit equation, we arrive at the following result. y double,m = mλd d ; y D (4) Double Slit Interference Pattern Page 4 of 6

5 Double Slit Interference and Diffraction Pattern Procedure II 1.) Switch the single slit accessory with the multiple slit accessory. You may need to adjust the laser. 2.) Once again, rotate through the variable slit area and observe how the pattern changes as you adjust the slit separation. Comment on what you observe (and include it in your final report). 3.) Measure the distance between the slit to viewing screen, D double. 4.) Similar to Part I, mark and measure the interference minima for the double slit configurations: a = 0.04 mm and d = mm, 0.25 mm, 0.5 mm. It might be hard to find the 3 configurations on the disk - if you are having trouble, ask your TA for help. Analysis II 1.) Determine the distance from the central maxima y double,m by halving the measured distances between minima. 2.) On a single graph, plot inverse slit separation, 1, versus distance from central maxima, d y double,m, for both order of minima. 3.) Apply a linear fit to both the data sets and comment on how their slopes compare to one another. What was expected? 4.) From the plot, make a statement about how slit separation and the distance between minima are related. 5.) What would you observe if you made the slit separation very very large (assuming you still had a coherent source passing through both slits). Comment on how this is different from the single slit experiment. Page 5 of 6

6 6.) Rotate back to the variable slit region and set it to an arbitrary slit separation. Using the procedure above, and the plot you made, determine the slit separation you had set. Wrap Up The following questions are designed to make sure that you understand the physics implications of the experiment and also to extend your knowledge of the physical concepts covered. Each member of your group should be able to answer any/all of these questions. Your TA will check that this is the case; please check out with your TA before exiting lab. 1.) What happens if you change the slit width for a double slit experiment. Make a hypothesis and then investigate by doing the following: (a) On the multiple split disk, locate the comparison of single slit and double slit. You might have to adjust the laser position such that both patterns appear on the screen. Comment on the differences and similarities you observe making note of the parameters a and d. (b) Next on the same disk, locate the comparison of two double slits with different slit widths. Again, you may have to adjust the laser position to see both patterns. What do you observe? (c) Make a statement about how slit width affects the pattern observed in double slit experiments. Last Few Steps 1.) Save any data/plots (in any format) with an easily identifiable name. 2.) Submit your data file to your group submission folder on D2L. 3.) Once this is complete and are certain that the data is saved, restart the computer when all experiments are completed. 4.) Tidy up your work station by turning off the lasers and ensuring the station is ready for your fellow students in other sections. Page 6 of 6