22 1 Model Two closely spaced slits produce a double slit interference pattern Visualize The interference pattern looks like the photograph of Figure 22 3 b It is symmetrical with the m 2 fringes on both sides of and equally distant from the central maximum Solve The bright fringes occur at angles m such that d m m 0 1 2 3 sin m 9 2 500 10 m 50 10 m 6 sin 2 0 02 2 0 020 rad 0 020 rad 1 15 180 rad 22 2 Model Two closely spaced slits produce a double slit interference pattern Visualize The interference pattern looks like the photograph of Figure 22 3 b It is symmetrical with the m 2 fringes on both sides of and equally distant from the central maximum Solve The two paths from the two slits to the m 2 bright fringe differ by r where 1 r 2 r r m 2 2 500 nm 1000 nm Thus the position of the m 2 bright fringe is 1000 nm farther away from the more distant slit than from the nearer slit 22 3 Model Two closely spaced slits produce a double slit interference pattern Visualize The interference pattern looks like the photograph of Figure 22 3 b sin Solve The bright fringes are located at positions given by Equation 22 4 d m For the m 3 bright m orange fringe the interference condition is d sin 3 3 600 10 m 9 For the m 4 bright fringe the condition is d 4 4 sin Because the position of the fringes is the same d sin d 3 sin 4 4 3 600 10 m 9 600 10 m 450 nm 9 3 4 22 4 Model Two closely spaced slits produce a double slit interference pattern Visualize The interference pattern looks like the photograph of Figure 22 3 b Solve The formula for fringe spacing is L d y 1 8 10 m 600 10 m 9 3 L d L d 3000 The wavelength is now changed to 400 nm and Applying the above equation once again L d being a part of the experimental setup stays the same y L d 9 400 10 m 3000 1 2 mm 22 5 Visualize The fringe spacing for a double slit pattern is y We are given L 2 0 m and L d 600 nm Solve Solve the equation for d We also see from the figure that y 1 3 cm d L y 9 600 10 m 2 0 m 2 10 m 1 3 0 36 mm Assess 0 36 mm is a typical slit spacing 22 6 Model Two closely spaced slits produce a double slit interference pattern Visualize The interference pattern looks like the photograph of Figure 22 3 b Solve The fringe spacing is L d d y L y 9 589 10 m 150 10 m 4 0 10 m 3 2 0 22 mm 22 7 Model Two closely spaced slits produce a double slit interference pattern Visualize The interference pattern looks like the photograph of Figure 22 3 b Solve The dark fringes are located at positions given by Equation 22 9 y m m 1 2 L d m 0 1 2 3 y 5 y 1 5 1 2 1 1 2 6 0 10 m 3 L d L d 2 4 60 10 m 0 20 10 m 3 500 nm 22 8 Model Two closely spaced slits produce a double slit interference pattern Visualize The interference pattern looks like the photograph of Figure 22 3 b Solve In a span of 12 fringes there are 11 gaps between them The formula for the fringe spacing is y L d 3 52 10 m 11 9 633 10 m 3 0 m d d 0 40 mm Assess This is a reasonable distance between the slits ensuring d L 1 34 10 4 1 22 9 Model A diffraction grating produces an interference pattern Visualize The interference pattern looks like the diagram in Figure 22 8 Solve The bright constructive interference fringes are given by Equation 22 15 sin m m 0 1 2 m d sin 1 9 1 550 10 m 2 1 0 10 m 1000 0 055 1 3 2 sin 2 0 110 and 2 6 3 Likewise 22 10 Model A diffraction grating produces a series of constructive interference fringes at values of m determined by Equation 22 15 Solve We have d sin m m m 0 1 2 3 sin 20 0 d 1 and d 2 sin 2 Dividing these two equations sin 2 2sin 20 0 0 6840 2 43 2 22 11 Model A diffraction grating produces an interference pattern Visualize The interference pattern looks like the diagram in Figure 22 8 Solve The bright constructive interference fringes are given by Equation 22 15 d sin m m d m sin m 9 2 600 10 m sin 39 5 1 89 10 m 6 The number of lines in per millimeter is 1 10 m 1 89 10 m 530 6 3 22 12 Model A diffraction grating produces an interference pattern Visualize The interference pattern looks like the diagram in Figure 22 8 Solve The bright fringes are given by Equation 22 15 d sin m m m 0 1 2 3 d sin 1 1 d 1 sin The angle 1 can be obtained from geometry as follows tan 1 0 32 m 2 2 0 m 0 080 1 tan 1 0 080 4 57 Using sin 1 sin 4 57 0 07968 d 9 633 10 m 0 07968 7 9 m 22 13 Model A diffraction grating produces an interference pattern Visualize The interference pattern looks like the diagram of Figure 22 8 Solve The bright interference fringes are given by d sin m m m 0 1 2 3 The slit spacing is d 1 mm 500 2 00 10 m and m 1 For the red and blue light 6 1 red sin 1 9 656 10 m 2 00 10 m 6 19 15 1 blue sin 1 9 486 10 m 2 00 10 m 6 14 06 The distance between the fringes then is y y 1 red y 1 blue where y 1 red y 1 blue 1 5 m tan19 15 1 5 m tan14 06 0 521 m 0 376 m y 0 145 m 14 5 cm So 22 14 Model Assume the screen is centered behind the slit We actually want to solve for m but given the other data it is unlikely that we will get an integer from the equations for the edge of the screen so we will have to truncate our answer to get the largest order fringe on the screen Visualize Refer to Figure 22 7 Use Equation 22 15 and Equation 22 16 m We sin d y L tan m m m d and L 2 0 m 510 nm are given 500 mm fringe will occur exactly at the edge of the screen …
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