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# solutions_41 - PHY2061 R D Field Chapter 41 Solutions...

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PHY2061 R. D. Field Solutions Chapter 41 Page 1 of 10 Chapter 41 Solutions Problem 1: Light from a small region of a 100 Watt incandescent bulb passes through a yellow filter and then serves as the source for a Young’s double-slit interference experiment. Which of the following changes would cause the interference pattern to be more closely spaced? (a) Use a blue filter instead of a yellow filter (b) Use a 10 Watt bulb (c) Use a 500 Watt bulb (d) Move the bulb closer to the slits (e) Move the slits closer together Answer: (a) Use a blue filter instead of a yellow filter Solution: The angular position of the bright fringes is given by d m λ θ = sin . A more closely spaced pattern implies that for a given m, θ is smaller. Thus, we want to increase d or decrease λ and from problem 15 we see that λ blue < λ yellow . Problem 2: The characteristic yellow light of sodium lamps arises from two prominent wavelengths in its spectrum, at approximately 589.0 nm and 589.6 nm , respectively. The light passes through a double slit and falls on a screen 10 m away. If the slits are separated by a distance of 0.01 mm , how far apart are the two second-order bright fringes on the screen ( in mm )? Answer: 1.2 Solution: The position of the second order bright fringe ( constructive interference ) is given by d d m 2 sin = = , where I have set m = 2 and used the small angle approximation. We also know that

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PHY2061 R. D. Field Solutions Chapter 41 Page 2 of 10 tan θθ ≈= y L . The position of the second order bright fringe is thus L d y λ 2 = , and mm m m nm d L y y 2 . 1 10 ) 10 )( 6 . 0 ( 2 ) ( 2 5 1 2 1 2 = = = . Problem 3: A monochromatic light placed equal distance from two slits a distance d apart produces a central bright spot with a width of 1 cm on a screen located a distance L away, as shown in the figure . If the entire apparatus is immersed in a clear liquid with index of refraction n the width of the central bright spot shrinks to 0.75 cm . What is the index of refraction n of the clear liquid? (Note: assume L >> d) Answer: 1.33 Solution: We know that for double-slit interference the position of the first dark fringe is given by L y d = = θ tan 2 sin and hence the width, w , of the central bright spot is d L y w = = 2 and n n w w 1 0 0 1 2 1 2 = = = , where I used λ 1 = λ 0 and λ 2 = λ 0 /n where λ 0 is the vacuum wavelength.
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solutions_41 - PHY2061 R D Field Chapter 41 Solutions...

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