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Unformatted text preview: 3. (a) The condition for a minimum in a single-slit diﬀraction pattern is given by a sin θ = mλ, where a
is the slit width, λ is the wavelength, and m is an integer. For λ = λa and m = 1, the angle θ is
the same as for λ = λb and m = 2. Thus λa = 2λb .
(b) Let ma be the integer associated with a minimum in the pattern produced by light with wavelength
λa , and let mb be the integer associated with a minimum in the pattern produced by light with
wavelength λb . A minimum in one pattern coincides with a minimum in the other if they occur at
the same angle. This means ma λa = mb λb . Since λa = 2λb , the minima coincide if 2ma = mb .
Consequently, every other minimum of the λb pattern coincides with a minimum of the λa pattern. ...
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- Fall '08