[UPSC CSE 2026] Diffraction (Q227, 15M)

A monochromatic parallel beam of wavelength \lambda = 600\text{ nm} is incident on a single slit of width a = 0\cdot 3\text{ mm}. A convex lens of focal length f = 1\text{ m} forms the Fraunhofer diffraction pattern on a screen.

(i) Determine the angular width and linear width of the central maximum on the screen.

(ii) If the slit width is halved, explain quantitatively how diffraction pattern changes.

(iii) A second wavelength 450\text{ nm} is added. Will the minima of the two wavelengths coincide? Justify mathematically.