Final answer:
The minimum width of a single slit that will produce a first minimum for a wavelength λ is λ/2. If the single slit produces 50 minima, the minimum width would be 100λ, and for 1000 minima, the minimum width would be 2000λ.
Step-by-step explanation:
In order for a single slit to produce a first minimum for a wavelength λ, the minimum width of the slit must be equal to a half wavelength, or λ/2.
(b) If the single slit produces 50 minima, the minimum width can be calculated by using the formula
Width = (2λN)/m, where N is the number of minima, λ is the wavelength, and m is the order of the minimum. For the first minimum (m=1), the width would be (2λN)/m = (2λ*50)/1 = 100λ.
(c) Similarly, for 1000 minima, the width would be (2λN)/m = (2λ*1000)/1 = 2000λ.