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1 Chapter The Wave Nature of Light - Interference and Di raction Name: Lab Partner: Section:. Purpose This experiment will demonstrate that light can be considered as a wave. If light is a wave, then interference e ects should be observed between waves of coherent light.. Introduction The wave nature of light was firmly established by Thomas Young s experiment two centuries ago. Young s experiment consists of a screen with a single hole or slit and a second screen with two closely spaced holes or slits. The single aperture is used to create a light source which originates from a single point and is in phase with itself. (We will employ a laser to provide light which is in-phase.) This light illuminates the double slit (see Figure.). Light from the two slits then interferes on a screen producing a series of bright and dark fringes. Directly opposite the center between the slits, the light travels an equal distance to the screen and the light constructively interferes to produce a bright central maximum. At some angle, thedi erenceinthepathlength,,isgivenby: =dsin (.) For constructive interference, must be an integer number of wavelengths so: =m = dsin m =0,,, 3... (.) and sin = m d m =0,,, 3... (.3) 69

2 Figure.: Schematic diagram for two slit (Young s) interference. θ w/ θ θ path difference Figure.: Schematic diagram for single slit di raction. We can find the actual distance on the screen from the central maximum by using tan = Y or Y = L tan. For small angles ( L 5o or less) we can substitute sin for tan and: Y = Ltan = Lsin = m L d (.4) Asingleslitcanalsoproduceaninterferencepattern. Basically,onesideoftheslit interferes with the other side of the slit. Consider the case in Figure. of a single slit of width, w. The screen is far away. On the screen directly opposite the center of the slit, the light from the two edges will travel the same distance and thus produce a bright maximum. As we move to some angle, thelightfromthetopedgewillinterferedestructivelywiththe light from the center of the slit to produce a minimum in intensity. The path length di erence for the two rays shown is wsin. Thismustbe for the first destructive interference. Thus we have: w sin = (.5) 70

3 θ d θ path difference Figure.3: Schematic diagram for a multiple slit di raction grating. sin = w (.6) For path di erences that are 3, 5,etc.,wealsohavedestructiveinterference. Thusthe dark fringes appear at angles given by: sin = m w m =,, 3... (.7) A di raction grating consists of many small closely-spaced regularly spaced slits (see Figure.3). When the angle is such that the path length di erence, d sin, isaninteger number of wave lengths, there is construction interference. Thus: dsin = m (.8) sin = m d (.9) where d is the center to center spacing of the slits and m is an integer. When m is the maximum is called the first order maximum..3 Procedure In the following procedures, we will examine the interference e ects from a single slit (di raction or self interference), a double slit (Young s experiment) and a di raction grating (many slits). Table. shows the parameters for the single and double slits. The di raction grating has 600 lines/mm or a slit spacing of.667 x 0 6 mm. For each part of the experiment, the basic equipment setup is shown in Figure.4. The laser is aligned on the appropriate slit pattern in the slit pattern plate (or the di raction grating). At a distance ( meters) from the slit pattern, tape a piece of white paper to the wall so the interference pattern can be seen clearly and marked for measurements. Special Cautions: Never look directly into the laser. 7

4 Pattern No. slits Slit width (mm) Slit Spacing (mm) A 0.04 B 0.08 D E Table.: Slit parameters Figure.4: Basic setup for the laser and slit. The laser is aligned on various slits on the slit pattern plate or di raction grating in the holder. Do not touch the surface of the di raction pattern plate or the di raction grating. Handle both by the sides. Be careful when moving around the darkened room for the last part of the experiment..3. Single Slit Place the di raction pattern plate in the holder. Adjust the laser on the lab jack so the laser beam is perpendicular to the plate and intersects slit A. Tape a piece of paper on the wall.5 - m from the slit plate. Measure the distance from the slit plate to the paper. Distance from slit plate to paper You should be able to see three or four minima with the room lights o (see Figure.5). Mark the central maximum and the minima on the paper. Remove the paper and record the distance from the central maximum to the various minima in Table.. Calculate the slit width for each order (n =,, 3 etc.) of the di raction pattern and record the values in Table.. The wavelength of the laser light is 633 nm. 7

5 Intensity n = d Θ L Maximum Minimum y - - Single slit diffraction Figure.5: Single slit di raction. maximum. This figure shows several orders and the central n Minimum Position Calculated Slit Width 3 4 Table.: Slit A data. Calculate the average of your values for the slit width and compare to the given value of 0.04 mm %errorofaverageslitwidthwithstandardvalue Repeat the procedure for slit B and record the data in Table.3. n Minimum Position Calculated Slit Width 3 4 Table.3: Slit B data. Calculate the average of your values for the slit width and compare to the given value of 0.08 mm. %errorofaverageslitwidthwithstandardvalue 73

6 .3. Double Slit Adjust the laser beam to intersect slit D. Again tape a piece of paper to the wall and measure the distance from the slit plate to the paper. You should be able to see several fringes (see Figure.6). Mark the center of the central maximum and the other maxima. Remove the paper and record the distance from the central maximum to the various maxima in Table.4. Calculate the slit separation for each order (n =,, 3, 4, etc.) of the di raction pattern and record the values in Table.4. n Maximum Position Calculated Slit Separation Table.4: Slit D data. Calculate the average of your values for the slit separation and compare to the given value of 0.5 mm % error of average slit separation with standard value Repeat the procedure for slit E. Record the data in Table.5 n Maximum Position Calculated Slit Separation Table.5: Slit E data Calculate the average of your values for the slit separation and compare to the given value of 0.50 mm. % error of average slit separation with standard value 74

7 n = d Θ L y - - Double slit Figure.6: Double slit interference pattern showing two orders and the central maximum..3.3 Grating Set up the di raction grating so that the laser beam intersects the grating surface perpendicular to the surface. The resulting di raction pattern can be projected on a nearby wall (see Figure.7). You should be able to see maxima on each side of the central beam (maximum). Measure the distance to the wall. It is not necessary to tape paper to the wall for this part of the experiment. Measure and record the distance of the maxima from the central maximum in Table.6. Calculate and record the distance between slits for each observed order of the di raction pattern. Note the small angle approximation (sin = tan ) no longer applies. n Maximum Position Calculated Distance between Slit Table.6: Di raction grating data. Find the average slit separation from your measurements and calculate the percentage error to the given value of.667 x 0 6 m (600 lines/mm). %errorofaveragedistancebetweenslitswithstandardvalue 75

8 Θ L y n = - - Diffraction grating Figure.7: Di raction grating pattern showing two orders and the central maximum..3.4 Questions. If you hold the di raction grating up to a light source, why do you see a rainbow pattern?. With the two slit pattern, some maxima are brighter than others and the pattern repeats. Why? (Hint: the slit width is 0.04 mm). 3. Why does sound di ract much more than light when passing through the same opening?.4 Conclusion Write a detailed conclusion about what you have learned. Include all relevant numbers you have measured with errors. Sources of error should also be included. 76

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