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Unformatted text preview: 7. The condition for a minimum of intensity in a singleslit diﬀraction pattern is a sin θ = mλ, where a
is the slit width, λ is the wavelength, and m is an integer. To ﬁnd the angular position of the ﬁrst
minimum to one side of the central maximum, we set m = 1:
θ1 = sin−1 λ
a = sin−1 589 × 10−9 m
1.00 × 10−3 m = 5.89 × 10−4 rad . If D is the distance from the slit to the screen, the distance on the screen from the center of the pattern
to the minimum is
y1 = D tan θ1 = (3.00 m) tan(5.89 × 10−4 rad) = 1.767 × 10−3 m .
To ﬁnd the second minimum, we set m = 2:
θ2 = sin−1 2(589 × 10−9 m)
1.00 × 10−3 m = 1.178 × 10−3 rad . The distance from the center of the pattern to this second minimum is y2 = D tan θ2 = (3.00 m) tan(1.178×
10−3 rad) = 3.534 × 10−3 m. The separation of the two minima is ∆y = y2 − y1 = 3.534 mm − 1.767 mm =
1.77 mm. ...
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 Fall '08
 SPRUNGER
 Physics

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