PHYS 164 LAB #24 Interference of Light Waves Instrumental uncertainty 0.2 cm dX = dD = DATA & ANALYSIS Source Wavelength ltrue = 546.1 nm Part I. DIFFRACTION GRATING GRATING 1 100 l i nes/ mm ORDER m 1 2 3 GRATING 2 300 l i nes/ mm ORDER m 1 2 3 GRATING 3 600 l i nes/ mm ORDER m 1 2 3 N= d = 1/N = D= XL (cm) 2.5 5 7.6 1000 1.00E-03 44.4 XR (cm) 3.0 5.7 7.9 lines/cm cm cm Xavg (cm) 2.8 5.4 7.8 Grating constant Screen distance ± (cm) 0.2 0.2 0.2 N= d = 1/N = D= XL (cm) 4.7 9.3 14.4 3000 lines/cm cm 3.333E-04 cm 26.3 XR Xavg (cm) (cm) 4.5 4.6 8.7 9.0 12.3 13.4 Grating constant Screen distance ± (cm) 0.2 0.2 0.2 N= d = 1/N = D= XL (cm) 3.9 8.3 13.3 6000 lines/cm cm 1.667E-04 cm 9.8 XR Xavg (cm) (cm) 3.7 3.8 9.4 8.9 14.2 13.8 Grating constant Screen distance ± (cm) 0.2 0.2 0.2 tan q ± 0.06 0.12 0.17 0.00 0.01 0.01 tan q ± 0.17 0.34 0.51 0.01 0.01 0.01 tan q ± 0.39 0.90 1.40 0.02 0.03 0.03 6. Compare appearance of mercury spectrum w/ monochromatic source (use 600 lines/mm grating) Color diffracted most? Orange Color diffracted least? Part II. THIN-FILM INTERFERENCE 8. Make a sketch on a sheet of paper of the fringes 9. Describe effect on fringes by depressing one edge 10. Measure fringes over cm q (rad) 0.06 0.12 0.17 q (rad) 0.17 0.33 0.47 q (rad) 0.37 0.73 0.95  sin q ± 0.00 0.00 0.01 0.06 0.12 0.17 0.00 0.00 0.01  sin q ± 0.01 0.01 0.01 0.17 0.32 0.45 0.01 0.01 0.01  sin q ± 0.02 0.02 0.01 0.36 0.67 0.81 0.02 0.01 0.01 Purple lexp (nm) 618.2 598.2 573.2 ± (nm) 47.6 24.7 16.9 % Diff lexp (nm) 574.3 539.6 502.9 ± (nm) 26.3 12.6 7.5 % Diff lexp (nm) 602.5 558.5 452.4 ± (nm) 32.9 10.1 3.8 % Diff 13.2 9.5 5.0 5.2 1.2 7.9 10.3 2.3 17.2 Agree w/ Uncert ? No No No 570.6 573.5 556.3 Agree w/ Uncert ? No Yes No 548.0 552.2 510.4 Agree w/ Uncert ? No No No 569.6 548.4 448.6 66 #24 Interference of Light Waves Objective The objective of this experiment is to observe various manifestations of the interfer- ence of light waves. Introduction and Theory Because light has a wave nature it can exhibit the same phenomena that, say, water waves do when they interact with sharp boundaries or with other waves. The effects of interaction include reflection, refraction, diffraction, and interference. The effects of dif- fraction and interference will be the subject of this laboratory. I. The Diffraction Grating The diffraction grating consists of a very large number of fine, equally spaced paral- lel slits. There are two types of diffraction gratings: the reflecting type and the transmit- ting type. The lines of the reflection grating are ruled on a polished metal surface: the incident light is reflected from the unruled portions. The lines of the transmission grating are rule on glass: the unruled portions of the glass act as slits. Gratings have typically be- tween 100 to 800 lines per millimeter. A diffraction grating provides the simplest and most accurate method for measuring wavelengths of light. The principles of diffraction and interference are applied to the measurement of wavelengths with a diffraction grating. Let the vertical broken line in Fig. 24.1 represent a magnified portion of a diffraction grating. Let a beam of parallel monochromatic light, originally from a single source and having passed through a slit, impinge upon the grating from the left. By Huygens' principle, the light spreads out in every direction from the ap- ertures of the grating, each of which acts as a separate new source of light. The envelope of the secondary wavelets determines the position of the advancing wave. In Fig. 24.1 we see the instantaneous positions of several successive wavelets after they have advanced beyond the grating. Lines drawn tangent to these wavelets connect points which are in phase: hence they represent the new wave fronts. One of these wave fronts is tangent to wavelets which have all advanced the same distance from the slits, and the wave front formed is thus parallel to the original wave front. A converging lens placed in the path of these rays would form the central image. Another wave front is tangent to wavelets whose distances from adjacent slits differ by one wavelength. This wave front advances in the direction 1 and forms the first-order image. The next wave front is tangent to wavelets whose distances from adjacent slits differ by two wavelengths. This wave front advances in the direction 2 and forms the second-order image. Images of higher orders will be found at correspondingly greater angles. 67 Max Max Max Incident wave Max S2 Max Max Max Max Max Si Max Max Max Max G B Fig. 24.1. Interference patterns resulting from waves incident on two slits of a grating Let a be the wavelength of the light, m the order of the image (m= 1 for the first- order image, m= 2 for the second-order image, etc.) formed on either side of the central (m= 0) image, d the distance between slits (a diffraction grating consists of several equal- ly-spaced slits), and the angle of deviation from the original direction of the light. These four quantities are interrelated by the grating equation, m2 = d sin e (24.1) The angle O is measured directly, while the grating constant d is calculated from the number of lines per millimeter ruled on the grating. If the light is monochromatic, a single image of the slit will appear in each order. - Grating 2 12 11 Source e Y -Slit 11 Observer 12 Fig. 24.2 Viewing diffraction-produced (virtual) images of a slit through a grating. 68 If the light is polychromatic, however, there will be as many images of the slit in each order as there are different wavelengths in the light from the source, the diffracting angle for each wavelength being given by the above equation. The resulting pattern of multiple lines in the first order is known as the first-order spectrum, that in the second order is the second-order spectrum, and so on. Spectra produced in this manner will be discussed in detail in Experiment #24. ng 723 12 1 CZ TO Fig. 24.3. Interference of two beams incident on the left and right boundaries of a thin film. UP TO II. Thin-Film Interference Interference is the combining by superposition of two or more waves that meet at one point in space. Thin-film interference can be understood as the combining by super- position of rays reflected from opposite sides of the thin film. Examples of thin films are soap films, lens coatings, or a thin wedge of air formed between two glass plates as shown in Fig. 24.3. Ray rı is reflected from the left surface of the film and ray r2 is reflected from the right surface. If t is the thickness of the air wedge at the point where ray rı strikes it, then ray r2 will travel a distance 2t further than ray r1. Therefore, if the rays were in phase be- fore they reached the wedge, when they combine they will no longer be in phase. Three effects must be taken into account in determining the net result of this type of superposition. First, not only does a ray undergo a partial reflection when encountering another medium (glass-to-air or air-to-glass), but it may also experience a 180° phase shift (which corresponds to a shift of X/2 in the wavetrain). A 180° phase shift occurs whenever the index of refraction of the first medium is less than that of the second (e.g., air-to- glass). Such a change of phase does not occur, however, when the index of refraction of the first medium is greater than that of the second (e.g., glass-to-air). Because of this ef- fect, the two rays will travel essentially the same distance (assuming t
Purchase answer to see full attachment