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Chapter5_6

# Chapter5_6 - sin cos 2 Î Ï€ d Ae r t kr i tot âˆ’ = Î¨ The...

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PHY3063 R. D. Field Department of Physics Chapter5_6.doc University of Florida Double Slit Intensity Pattern We form the superposition of the two waves at the point P on the screen as follows. 2 1 ) ( 2 ) ( 1 2 1 Ψ + Ψ = Ψ = Ψ = Ψ tot t kr i t kr i Ae Ae ω and thus () ( ) ) cos( 2 1 2 1 2 / ) ( 2 / 2 / 2 / ) ( ) ( ) ( ) ( 2 1 1 1 1 2 1 r k e Ae e e e Ae e Ae Ae Ae r ik t kr i r ik r ik r ik t kr i r ik t kr i t kr i t kr i tot = + = + = + = Ψ + Ψ = Ψ where k = 2 π / λ . The path difference (for L >> d ) is given by θ sin 1 2 d r r r = = The distance from the center of the two slits and the point P on the screen is given by r = r 1 + r/2 and hence
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Unformatted text preview: ) / sin cos( 2 ) , ( ) ( Î» Ï€ d Ae r t kr i tot âˆ’ = Î¨ . The intensity is proportional to the amplitude squared and hence ) / sin ( cos 4 ) ( 2 d I I = where I is the intensity of a single wave (wave 1 or wave 2). S 1 r 2 S 2 r 1 d Î¸ Double Slit Î¸ âˆ† r =d sin Î¸ S 1 Î¸ S 2 d L Double Slit Intensity r 1/2 1/2 1-1/2 d sin / 2 5/2-1-3/2-2 P Central Bright Spot...
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