How would the interference pattern change if a blue laser was used instead of a red laser? The width of the interference pattern would be expanded The width of the interference pattern would be compressed The peak intensities of the interference pattern would be expanded The peak intensities of the interference pattern would be compressed For a single slit, what does decreasing the slit width do to the intensity curve (select all that apply)? Increases the width of the intensity curve Decreases the width of the intensity curve Decreases the height of the intensity curve Increases the height of the intensity curve For a single slit, the manual asks you to plot ym as a function of %. What is the slope of this graph? gm (1 m. DA A D A For a double slit, which of the following statements are true (select all that apply)? The slit separation determines the positions and widths of the envelope The slit separation determines the positions and widths of the intensity peaks The slit width determines the positions and widths of the intensity peaks The slit width determines the positions and widths of the envelope EXPERIMENT DIFFRACTION OF LIGHT lntrod uction: When light or any other type of wave passes through an opening or goes by the edge of an obstacle, the wave extends {bends} into the region not directly exposed to the wave front. This phenomenon is called diffraction. An explanation of this effect was first proposed by Huygens (1629 1695}, a contemporary of Newton, in the light of a wave theory of light. Huygens' principle states that every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The new wave front is the envelope of all the wavelets. So, when a wave front arrives at an opening, each point along the part of the wave front that extends across the opening sends out wavelets, all in phase, which spread out in all directions. The wave theory of light was not always widely accepted. In the early 1800's, the great scientist Poisson [1?81 1840}, a wave-theory deti'actor, pointed out what he thought was an obvious aw with the theory, namely that it predicted a bright spot would occur at the center of the shadow created by a circular object! The experiment was performed and the spot was found! It is observed that a wave passing through a slit does not illuminate the region beyond the slit uniformly, but creates bands of high and low intensity. This phenomenon is known as interference, and occurs when two or more waves arrive at the same point simultaneously. The resulting light intensity at that point will depend on the relative phase of the component waves. [For example, waves which arrive in phase add to give a large intensity; waves which arrive out of phase cancel.) In the Huygens model, the large number of wavelets produced by each of the sources interfere with one another and result in an interference pattem. In this experiment, a diffraction pattern is created by allowing the light emitted by a diode laser to fall onto a slit. The entire pattern can be observed by placing a piece of paper [or some other white screen) on the far side of the slit, or can be examined point by point by having the light pass through an aperture onto a light sensor. The light sensor is mounted on a carriage which slides sideways [i.e. perpendicular to the optics bench) using a thumbwheel. There is a two-position switch on the top of the sensor which controls the gain. [If the signal is too weak, turn it up, and if it is too strong, turn it down.) The slit disks consist of the Single Slit Disk and the Multiple Slit Disk and should be placed in a holder about 3 cm in front of the laser. They carry many slit systems of different sizes and shapes. Each disk is mounted on a frame in such a way that any of the slits can be rotated in front of the laser. The frame can be rotated in its mount slightly for better alignment. The entire mount can be removed from the optical bench for better viewing. An aperture disk in front of the detector is used to keep out stray light and to better define the position of the incoming beam. The disk has many apertures of various shapes and sizes to choose from. Choosing an aperture is a balancing act between intensity and resolution: as the aperture narrows, the spatial resolution increases, but the intensity decreases. The experiment utilizes a computer interface and software to collect and analyze your diffraction patterns. The output of the light sensor is an electrical signal which is proportional to the intensity of the light falling on the detector. A second sensor in the carriage, called a rotary motion sensor, monitors the motion of the thumbwheel and so is able to measure the relative position of the sensor along the rack. The output of the sensors are fed simultaneously to an interfacei'software which generate a plot of the intensity as a function of position. Exercise 1: Qualitative Study >Never look directly into a laser beam. Avoid accidents by keeping your head out of the plane of the beam: try to work from above and to the side, looking away from the source. Be alert to the possibility of reflections from polished surfaces. Begin by setting up the apparatus as shown in Figure 2. You may find it useful to turn the diode laser on and adjust the beam height so that it points into the light sensor (i.e. at the center of the bottom line of the aperture disk) before placing the slit disk in the beam path. You can flip through the various slit systems on the slit disks while looking at the diffraction patterns on the screen (it might help to have the lights dimmed). Try to discern some of the general features of the pattern. For example, how does the geometry of the pattern compare to the geometry of the slit? As you go from a narrow slit to a wide slit, what happens to the pattern? Does the complexity of the pattern correlate with the number of slits? >When you have a good sense of the physical system, move on to the quantitative measurements.Exercise 2: Single Slit 5* Imagine a coherent light source incident on a single slit of width :1 and observed on a screen at some relatively large separation from the slit. The interference pattern from such an arrangement is shown in Fig.2, Notice that there is a very intense region (called the central maximum) directly opposite the slit, as might be expected. However on either side of this region the intensity goes to zero, and away from the central maximum. on either side. are weaker subsidiary maxi l . incoming beam (It = 650 um) screen (detector) Figure 3: Single Slit Diffraction Pattern > When diffraction of light occurs as it passes through a slit, the angle to the minima in the diffraction pattern, where the wavelets arrive out of phase and cancel each other completely, is given by asin9= ml [m= 1,2,3, ...) Minima where a is the slit width, Sis the angle from the center of the pattern to the mu\" minimum, ('1'. is the wavelength of the incident light, and m is the order (1 for the first minimum, 2 for the second minimum, counting from the center out}. See Fig.2. 3? Place the Single Slit Disk in its holder about 3 cm in front of the laser. On the slit disk, you will find a set of four single slits of different widths. Collect a good diffraction pattern from each of the slits by pressing record, sliding the sensor assembly from one side to the other. and pressing stop. Remember that the vertical scale is essentially arbitrary. How are the patterns similar'.J How are they different? Where you can see more than one peak. how are the peaks spaced? > The dominant feature of the single slit pattern is the central peak and you may have noticed that its width changes from one pattern to the next. Use the cursor to determine the distances from the central peak to the minima on either side of it (Make sure that you include an estimate of the uncertainty). You will need to measure the slit to detector distance D for the analysis. > Include a plot ofthe diffraction pattern from one ofthe wider slits. where more detail is visible. in your report. 5' Plot ym (the distance from the center to the mth minimum) as a function of rule. You can improve your results by averaging the left and right sides of the pattern. i.e. nd y, by dividing the width of the central peak of the diffraction pattern by 2, and y; by dividing the distance from the second zero on the le to the second zero on the right by 2, etc. Depending on the apparatus' sensitivity, the slit you choose, the aperture disk setting, etc., sometimes you might only get one point from a particular slit thickness, sometimes you might get many points. Include them all. You should also > (i=650nm) > use the approximation sinG E tant9 = y / D. Find the best tting straight line and from the slope find the wave length of the laser light {1 used in this experiment. Compare this value of 2?. with the manufacturer's value of 650 nm. Exercise 3: Double Slit When light passes through two slits (with two characteristic lengths: the slit width and the slit separation), the two light rays emerging from the slits interfere with each other and produce interference fringes. The angle to the maxima (bright fringes} in the interference pattem is given by rising = m It [m=0, 1,2, 3, ...} Maxima where d is the slit separation, Qis the angle from the center of the patter-11 to the mth maximum, 21'. is the wavelength of the incident light, and m is the order (0 for the central maximum, 1 for the first side maximum, 2 for the second side maximum, counting from the center out). Note that the envelope of the intensity curve looks like a single slit diffraction pattem, determined by the width ofthe slits. See Fig.3. anmamm qwssss" "' double [nten sity - slit incoming Diffraction beam envelope Figure 4: Interference Fringes screen ( detector ) Place the Multiple Slit Disk in the track. You will notice that it holds several double slit patterns of different widths and separations. You might begin by qualitative comparison of the patterns created by single slit and double slit systems of the same width by using the \"COMPARISONS\" part of the Multiple Slit Disk [but don't try to capture data with this part of the disk; if two diffraction patterns enter the sensor at the same time the graph will be the sum of the two). Again, adjusting the aperture to equalize the intensities may make the comparison easier. For the double slit systems, investigate the effect of changing the slit separation, keeping the width fixed, and the effect of changing the slit width, keeping the separation fixed. Save appropriate figures to demonstrate the differences, and comment on them. This time we will use the known wavelength in order to find the slit separation. For one particular graph that you choose, use 1 = 650 nm and your peak separations to find 49'. Compare it to the real slit separation that you used, and make sure to include uncertainty. Show that d "=- 11 m D /y for D >> y , where d is the slit separation, A is the wavelength of the incident light, in is the order, D is the slit to detector distance, and y is the distance from the central peak to a subsidiary peak. Experiment Setup Accessories Slit Accessories: Single and Multiple Slit Sets Diode Laser Two slit accessory disks offer a variety of single and multiple slits for diffraction experiments. The two accessory disks are mounted to lens holders. Just rotate the disk for a wide range of diffraction patterns. The slit patterns automatically align with the laser. The Slit Accessory includes Single and Multiple Slit Disks attached to optics bench mounts. Single Slit Disk: 4 single slits, 2 circles, l linefslit comparison, 4 two-dimensional diffraction patterns variable-width slit [0.02-0.20 m), l opaque line. Multiple Slit Disk: 4 double slits, 4 multiple slits (2, 3, 4, or 5 slits), 4 singlez'double slit comparisons, variable double slit [slit separation 0.125-03'5 mm}. Diode Laser: The Diode Laser is mounted in a lens holder at just the right height for use with the Slit Accessory. Vertical and horizontal adjustments align the beam for the clearest interference patterns. The Diode Laser includes a 9 V Adapter. Specications: Output Power