A monochromatic plane wave of wavelength 550nm is incident normally on three separate screens, each containing parallel narrow openings spaced by the same distance d.
• Screen I has exactly two slits (a traditional double-slit).
• Screen II has three slits.
• Screen III is a section of a transmission grating that contains 200 identical slits within the illuminated region.
An adjustable detector far from the screens records the intensity I(θ) as a function of the angle θ measured from the central (perpendicular) direction.
(a) Describe qualitatively how the angular width of a principal maximum changes as the number of illuminated slits increases from 2 to 3 to 200. Clearly connect your explanation to the way individual wave amplitudes combine at the detector.
(b) The peak intensity of the central maximum is observed to increase dramatically between Screen I and Screen III, even though the total optical power emerging from each screen is the same. Explain how conservation of energy is satisfied in this situation.
(c) Contrast the relative prominence of secondary (side) maxima for the three screens. Include in your discussion the physical origin of these secondary peaks and why their heights change with slit number.