1. (a) The condition for a minimum in a single-slit diffraction pattern is given by asin θ= mλ, where ais the slit width, λis the wavelength, and mis an integer. For λ= λaand m= 1, the angle θis the same as for λ= λband m= 2. Thus, λa= 2λb= 2(350 nm) = 700 nm. (b) Let mabe the integer associated with a minimum in the pattern produced by light with wavelength λa, and let mbbe 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 maλa= mbλb. Since λa= 2λb, the minima coincide if 2ma= mb. Consequently, every other minimum of the λbpattern coincides with a minimum of the λapattern. With ma=2, we havemb= 4. (c) With ma=3, we havemb= 6.
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