p37_003 - 3. (a) The condition for a minimum in a...

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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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