inal answer:
The minimum slit width for a single slit to produce the first diffraction minimum is equal to the light's wavelength. For 50 minima, it is 50 times the wavelength, and for 1000 minima, it is 1000 times the wavelength.
Step-by-step explanation:
The single slit diffraction pattern is determined by the width of the slit and the wavelength of the light. We can find the minimum width of the slit that will produce a first minimum using the formula for single slit diffraction minima: d sin(\theta) = m\lambda, where d is the slit width, \( \theta \) is the angle of diffraction, m is the order number (for the first minimum, \( m = 1 \)), and \lambda is the wavelength of the light.
(a) For the first minimum (m = 1), the minimum width of the slit is d = \lambda. Thus, the minimum width is equal to the wavelength of the light.
(b) For the 50th minimum (m = 50), the slit width will be d = 50\lambda, which is 50 times the wavelength of the light.
(c) Similarly, for producing 1000 minima (m = 1000), the slit width would need to be d = 1000\lambda, or 1000 times the wavelength.