[UPSC CSE 2026] Interference (Q167, 10M)

A Fabry--P'erot interferometer is illuminated by monochromatic light of wavelength \lambda = 500\text{ nm}. The mirror separation is d = 0\cdot 8\text{ mm}. It is observed that two successive transmitted maxima correspond to wavelengths \lambda and \lambda + \Delta\lambda, both satisfying the condition for normal incidence. Determine the smallest wavelength difference \Delta\lambda that can be resolved by the interferometer. Explain physically why this quantity depends on mirror separation.