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Unformatted text preview: 110. The derivation is similar to that used to obtain Eq. 3627. At the first minimum
beyond the mth principal maximum, two waves from adjacent slits have a phase
difference of ∆φ = 2πm + (2π/N), where N is the number of slits. This implies a
difference in path length of
∆L = (∆φ/2π)λ = mλ + (λ/N). If θm is the angular position of the mth maximum, then the difference in path length is
also given by ∆L = d sin(θm + ∆θ). Thus
d sin (θm + ∆θ) = mλ + (λ/N). We use the trigonometric identity
sin(θm + ∆θ) = sin θm cos ∆θ + cos θm sin ∆θ.
Since ∆θ is small, we may approximate sin ∆θ by ∆θ in radians and cos ∆θ by unity.
Thus,
d sin θm + d ∆θ cos θm = mλ + (λ/N). We use the condition d sin θm = mλ to obtain d ∆θ cos θm = λ/N and
∆θ = λ
.
N d cosθ m ...
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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