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Unformatted text preview: 43. The derivation is similar to that used to obtain Eq. 3724. 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 cos θm ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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