![]() By using closely spaced slits, the light is diffracted to large angles, and measurements can be made more e accurately. However, a diffraction grating has many slits, rather than two, and the slits are very closely spaced. In theory, they en on function much the same as two-slit A pacing 600 slitsom apertures. Combining an earlier equation with the previous one, it can be shown that AB sin (tan-a)=ni (1) and solving for the wavelength of the incident light we find 1 = sin(tan- )) (2) The Diffraction Grating Diffraction gratings are used to make very accurate measurements of the Color Image -An-Anlatan ) wavelength of light. You need only to measure the value of for a particular value of n to determine the wavelength of the lightīlonde Duration Pune Figure PN10.1: Geometry of Two-SP Interference To measure, notice that the dotted lines in the illustration show a projection of the interference pattern onto the Diffraction Scale (as it appears when looking through the slits). (Ask you lab instructor about the spacing between the sits, AB). From right triangle ACB, it can be seen that BCAB sine = n2. At the zeroth maxima, light rays from slits A and B have traveled the same distance from the slits to the plate, so they are in phase and interfere constructively At the first order maxima (to the left of the viewer), light from slit B has traveled one wavelength farther than light from slit A, so the rays are again in phase, and constructive interference occurs at this position as well At the nth order maxima, the light from slit B has traveled n wavelengths farther than the light from Slit A, SO again, constructive interference occurs. The essential geometry of the experiment is shown in Figure PH10.1. ![]() Where the wave fronts from two sources overlap, an interference pattern is formed. Since the slits are illuminated by the same wave front, these sources are in phase. As Hyugen's principle tells us, each slit acts as a new source of light. In two sit interference, light falls on an opaque screen with two closely spaced, narrow slits. ![]() In fact, in this experiment you will measure the wavelength of light, and see how that wavelength varies with color. Two-Slit Interference In certain circumstances, light behaves exactly as if it were a wave. At any position on your viewing screen, determine the phase of the light contributed by each point on the aperture and finally, use the superposition principle-the net displacement caused by a combination of woves is the algebraic sum of the displacement caused by each individual wave-to sum the contributions from all points on the aperture. Simply treat each aperture as a collection of point sources of light (small, closely packed points will give the best approximation of the diffraction pattern). The diffraction pattern created by a particular aperture can be determined quantitatively using Huygen's principle-when light acts as a wave, each slit in on aperture acts as a source of new waves. However, any aperture, or collection of apertures, will produce a diffraction pattern if the dimensions of the apertures are of the same order of magnitude as the wavelength of the visible light. Materials Pasco Introductory Optics Kit Diode Laser Power Supply 19V) Speed of Light Apparatus Oscilloscope Probe (2) Diode Laser Desk Lamp, 40W bulb maximum GW Instek GDS-1042 Oscilloscope Theory The simplest diffraction patterns are produced by narrow slits.Investigate the general principles involved in diffraction, and to examine how these principles are affected by slit interference, aperture size, pattern and diffraction gratings Determine experimentally the speed of light.Data Table 1 Two-Slit Interference Slit Spacing for Pattern D (AB) Distance from Diffraction Plate to Diffraction 0.125 mm Scale (L) 0.575 m (nm) Left of Central Maxima (m) 0.0025 0.0055 0.0085 0.0119 0.0145 (nm) 0.0030 Right of 0.0055 Central 0.0090 Maxima 10.0120 5 0.0150 Average Wavelength for the Laser (ave) nm Data Table 2 Diffraction Grating Number of Lines Distance from Diffraction Plate to Diffraction 600 lines/mm 7 Scale (L) 0.07 m (nm) 1 0.033 Left of Central Maxima 0.098 (nm) Right of 0.0825 Central Maxima 2 0.096 Average Wavelength for the Laser (ve) Percent Difference for Wavelength from Part A nmĢ.99 x108 m/s 1.5 Data Table 3 Speed of Light Speed of Light (c) Refractive Index of Optical Fiber (n) Length of Optical Fiber Transmission Peak Time Receiver Peak Time Calculated Speed of Light Percent Error 25 127 20 m ns ns m/s m/s Adjusted Speed of Light Adjusted Percent Error
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