A narrow rectangular slit of width 0.080mm is illuminated by red light of wavelength 632nm. A viewing screen is placed 1.5m from the slit, and the resulting diffraction pattern is observed.
(a) Calculate the perpendicular distance on the screen between the center of the central bright band and the third dark band above it.
(b) Determine the angular position, measured from the central axis, of the third dark band found in part (a). Evaluate whether the small-angle approximation used in your calculation is justified.
(c) Without re-calculating the angle, predict the new distance between the same two points on the screen if the screen is moved to 3.0m from the slit. Explain your reasoning clearly.