ch36-p110 - 110. The derivation is similar to that used to...

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Unformatted text preview: 110. The derivation is similar to that used to obtain Eq. 36-27. 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.

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