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CHAPTER 37 INTERFERENCE AND DIFFRACTION - - . -- Section 37-2: Double-Slit Interference Section 37-3: Multiple-Slit Interference and Diffraction Gratings Problem Problem 3. A double-slit experiment has slit spacing 0.12 mm. (a) What should be the slit-tc-screen distance L if 13. In a 5-slit system, how many minima lie betwee* the bright fringes are to be 5.0 mm apart when the the zeroth-order and first-order maxima? slits are illuminated with 633-nm laser light? (b) What will be the fringe spacing with 480-nm light? Solution The particular geometry of this type of double-slit experiment is described in the paragraphs preceding Equations 37-2a and b. (a) The spacing of bright fringes on the screen is Ay = XL/d, so L = (0.12 mm)(5 __ - mm)/(633 nm] = 94.8 cm. (b) For two different wavelengths, the ratio of the spacings is ayf/Ay = Af/A; therefore Ay' = (5 mm)(480/633) = 3.79 mm. Problem 7. Light shines on a pair of slits whose spacing is three times the wavelength. Find the locations of the first- and second-order bright fringes on a screen 50 cm from the slits. Hint: Do Equations 37-2 apply7 Solution Since d = 3X, the angles are not small, and Equa- tions 37-2 do not apply. The interference maxima occur at angles given by Equation 37-la, 6' = sin-](mX/d) = sill-'(m/3), so only two orders are present, for values of m = 1 and 2 (6' < 90'). If we assume that the slit/screen geometry is as shown in Fig. 37-6, then y = L tan 6' = L tan(sin-' (77213)) = ~m/ Jw. (Consider a right triangle with hypotenuse of 3 and opposite side m, or use tan = sin 6'1 dm.) For m = 1 and 2, and L = 50 cm, this gives yl = (50 cm)(l/&) = 17.7 cm, and yz = (50 cm)(2/4) = 44.7 cm. Problem 9. For a double-slit experiment with slit spacing 0.25 mm and wavelength 600 nm, at what angular position is the path difference equal to one-fourth of the wavelength? Solution If we set the path difference equal to a quarter wavelength, we obtain d sin = X/4, or w sin = 600 nm/4(0.25 mm) = 6x10~~ rad - 0.0344".
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This note was uploaded on 12/03/2009 for the course PHYS 2c taught by Professor Wurthmeir during the Spring '05 term at UCSD.

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