A monochromatic laser beam of wavelength 550nm is incident on a narrow single slit of width 0.15mm. A screen is placed 2.4m from the slit, and its surface is oriented perpendicular to the incident beam. The center of the slit is aligned with the midpoint of the screen.
Beginning at the line directly opposite the slit, the screen extends 5.0cm upward and 5.0cm downward.
(a) Determine the highest–order dark fringe that appears on the portion of the screen located above the central axis.
(b) Calculate the total number of dark fringes (diffraction minima) that can be observed on the full height of the screen, counting those above and below the central axis but excluding the central bright region itself.