PHY2061 R. D. Field Department of Physics chp42_3.doc University of Florida Single-Slit Diffraction Intensity Pattern (2) The overall wave function at the point Pon the screen is given by )sin()sin(21212/)1(111φφφωω∆∆==Ψ=Ψ∆−−−=∑NeeAeSeAeNiikrtNikrtiNnnN. The distance where rfrom the center of the slit to the point Pis given by, φθ∆−+=+=)1(sin211211NrWrrk. Now as Nbecomes large φφ∆ →∆−=∆Φ>>NNN1)1(and ∆Φ∆Φ≈∆Φ∆Φ≈∆∆=Ψ−−−2121)(2121)(2121)()sin()/sin()sin()sin()sin(tkritkritkriNNAeNAeNAeωωωφφwhere I used NNN22sin1∆Φ →∆Φ>>. Thus for large N ∆Φ∆Φ≈Ψ−2121)()sin()
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