Consider a laboratory setup in which a single-slit diffraction pattern is observed on a screen that subtends a fixed angular window of ±10∘ about the central axis. Assume that all other experimental parameters (distance to the screen, alignment, and environmental conditions) remain unchanged.
(a) Predict qualitatively how the number of dark fringes observable within the window changes if the slit width is reduced to one-half of its original value. Justify your prediction.
(b) Predict qualitatively how the number of dark fringes observable within the same window changes if, instead of altering the slit, the wavelength of the incident light is doubled while the slit width is left unchanged. Justify your prediction.