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Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 25
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PAL #24 Diffraction Single slit diffraction, how bright is spot 5 cm from center? = 680 nm, a = 0.25 mm, D = 5.5 m tan = y/D, = arctan (y/D) = 0.52 deg = ( a/ )sin = 10.5 rad I = I m (sin / ) 2 = Nearest minima What is m for our ? a sin = m m = Between 3 and 4, closer to 3
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Double Slit Diffraction Each maxima had the same peak intensity In single slit diffraction we produced a wide, bright central maximum and weaker side maxima The interference maxima are modulated in intensity by a broad diffraction envelope
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Diffraction and Interference
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Double Slit Pattern The outer diffraction envelope is defined by: a sin =m Between two minima, instead of a broad diffraction maxima will be a pattern of interference fringes d sin = m a,d and are properties of the set-up, indicates a position on the screen and there are two separate m’s (one for the diffraction and one for the interference)
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Patterns e.g. You would expect the m = 5 interference maxima would be bright, but if it happens to fall on the m = 3 diffraction minima it will be dark What you see at a certain angle , depends on both of the m’s We can use the location of two adjacent diffraction minima (sequential diffraction m’s) to define a region in which may be several interference maxima i.e. first define the diffraction envelope, then find what interference orders are inside
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Diffraction Envelope
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Diffraction Dependencies For longer wavelengths, the fringes are further apart For solving diffraction/interference problems: Can find the diffraction minima with a sin =m Can find the interference maxima with d sin =m There are two different m’s
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Intensity The intensity in double slit diffraction is a combination of the diffraction factor: and the interference factor: The combined intensity is: I = I m (cos 2 ) [(sin / ] 2 Note that a and b are in radians
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Angle and Distance Note that for any interference or diffraction pattern you can translate between angles ( ) and distance on the screen (y) tan = y/D y D
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Next Time Read: 36.9
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If the width of the slit and the wavelength of light doubles, what happens to the space between minima? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled
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If the Hubble Space Telescope has an aperture of 2.4 meters and observes at 550 nm, what is the smallest angle it can resolve? a)3.4X10 -9 rad b)2.8X10 -7 rad c)0.005 rad d)0.6 rad e)279.5 rad
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