A student aligns a red laser (wavelength 650 nm) so that its beam passes through a narrow adjustable slit and forms a diffraction pattern on a screen 1.80 m away. The slit width is set so that the central bright maximum on the screen is exactly 12 cm wide.
The student then replaces the red laser with a green laser of wavelength 520 nm while keeping the screen in the same position. The slit assembly allows its width to be finely adjusted so that the central maximum remains 12 cm wide.
(a) Derive an algebraic expression that relates the new slit width to the original slit width and to the two laser wavelengths.
(b) If the original slit width with the red laser was 0.060 mm, calculate the slit width required when using the green laser so that the central maximum width remains 12 cm.
(c) Suppose the student forgets to adjust the slit width after switching to the green laser. Describe qualitatively how the central maximum would change and explain the physical reason for that change.