Do NOT write on these sheets or take them with you! The next class needs them too! PHYS-1200 PHYSICS II Class 20 Activity: Interference and Diffraction of Light Waves SOLUTION SPRING 2006 In this exercise, you will perform experiments to study the interference pattern of light that has been diffracted by passing through a single slit, and the interference pattern of light that has passed through a pair of slits (Young's experiment). At your table you should have: An optical track A red laser A set of various double slits, and a set of various single slits mounted on disks A mounted viewing screen with metric scale THE LASER IS NOT A TOY. AVOID LOOKING DIRECTLY INTO THE LASER, AND DO NOT POINT IT WHERE ITS LIGHT MIGHT ENCOUNTER ANYONE'S EYE(S) Single Slit Diffraction In single slit diffraction, the first minimum of the diffraction pattern occurs at an angle given by the formula, a sin = , (1) where a is the width of the slit, is the angle at which a minimum occurs, and wavelength of the light used in the experiment. is the Make a copy of the table below on your paper, and record all data and calculated results in that table. DO NOT WRITE ON THIS SHEET! Then follow the steps below the table. a (mm) Slit 1 Slit 2 0.04 0.08 D (mm) 600 600 y (mm) 9.5 5.0 sin 0.0158 0.00833 (nm) 633 667 1. Plug in the laser, and place it at the 200 mm mark on the optics bench. Place the single slit disk at the 300 mm mark on the bench, and place the screen at the 900 mm mark on the bench. In your table, record D the distance between the slit to the screen. 2. Align the beam so that it passes through the 0.04 mm single slit and produces a pattern on the screen. You may have to tilt the laser and/or rotate the slit wheel out of its locked position to achieve alignment On the viewing screen, measure the distance from the middle of the diffraction pattern to the first minimum. Record it in the table as y. (Hint: y is equal to one half the distance between the two minima on either side of the central <a href="/keyword/bright-spot/" >bright spot</a> .) The tics on the screen are mm; numbers are cm on this scale. If the pattern is not horizontal, turn the screen so its ruler is aligned with the pattern. I measured a full width of 19 mm, so y = 9.5 mm Turn the paper over. There is more on the back. Do NOT write on these sheets or take them with you! The next class needs them too! How does the width of the central <a href="/keyword/bright-spot/" >bright spot</a> compare with the width of the other <a href="/keyword/bright-spots/" ><a href="/keyword/bright-spot/" >bright spot</a> s</a> ? The central <a href="/keyword/bright-spot/" >bright spot</a> is twice as wide as the other <a href="/keyword/bright-spots/" ><a href="/keyword/bright-spot/" >bright spot</a> s</a> . 3. Calculate sin from the measurements. (Hint: Is sin tan ?) sin (9.5 mm)/(600 mm) 4. Use equation (1) to calculate the wavelength of the laser light. See the table. 5. Repeat the experiment for a = 0.08 mm. I measured a full width of 10 mm, so y = 5.0 mm sin (5.0 mm)/(600 mm) Double Slit Interference In double slit interference, interference maxima occur at angles given by the formula, d sin =m , (2) where d is the separation between the slits, is the angle at which a maximum occurs, m is an integer, and is the wavelength of the light used in the experiment. Make a copy of the table below on your paper, and record all data and calculated results in that table. DO NOT WRITE ON THIS SHEET! Then follow the steps below the table. d (mm) Pair 1 Pair 2 0.25 0.50 D (mm) 600 600 y (mm) 1.56 0.778 sin 0.00260 0.00130 (nm) 650 650 1. Replace the disk containing single slits with one containing double slits. Place it at the 300 mm mark, so D is the same as it was for the single slit experiment. 2. Set the slit wheel to the double slits with a = 0.04 mm and d = 0.25 mm. Align the beam so that it passes through the double slits and produces a pattern on the screen. The double slit pattern should appear as a series of closely spaced spots within the single slit pattern. Record D, the distance from the slits to the screen, in your table. 3. On the viewing screen, measure the distance from the middle of the interference pattern to the first interference maximum. Record it in the table as y. It should be easier, and more accurate, to measure the distance to a higher order maximum (e.g. m = 4 or 5), and divide the result by m. I went from one side to the other, and found that 9 fringes occupied 14 mm. y = (14 mm)/9 4. Calculate sin from the measurements. sin (1.56 mm)/(600 mm) 5. Use equation (2) to calculate the wavelength of the laser light. See the table. 6. Repeat the experiment for the pair of slits with a = 0.04 mm and d = 0.50 mm. 18 fringes occupied 14 mm, so y = (14 mm)/18 sin (0.778 mm)/(600 mm) Do NOT write on these sheets or take them with you! The next class needs them too! Conclusion You now have four measurements of the wavelength of the laser. Record the average of the four measurements, and the extreme spread of your measurements as a percent of the average. The extreme spread can be calculated as max min 100% . average avarage = 650 nm 667 mm 633 mm 100% = 5.2% 650 mm