Monochromatic light of wavelength 550nm illuminates a single rectangular slit 0.050mm wide.
Two separate screens are placed on the axis of the incident beam, one at distance L1=0.10m and the other at L2=5.0m, so that diffraction patterns can be recorded at both locations.
(a) Derive an approximate relationship between the distance ym on the screen from the central maximum to the m-th minimum, the slit width a, the wavelength, and the screen distance L, assuming the angles involved are small.
(b) Using your expression for m=1, calculate the angular position of the first minimum.
(c) Determine the linear distance from the central maximum to the first minimum for each screen, L1 and L2, and compare the two results.
(d) Discuss whether the far-field (Fraunhofer) approximation employed in part (a) is appropriate for each screen location. Support your answer by referencing the relative sizes of relevant physical quantities.