Question

A narrow slit is illuminated by a parallel beam of monochromatic light of wavelength λ equal to 6000 Å and the angular width of the central maximum in the resulting diffraction pattern is measured. When the slit is next illuminated by light of wavelength λ’, the angular width decreases by 30%. Calculate the value of the wavelength λ’.

Answer 1

Angular width 2φ = 2λ/d

Given λ = 6000 Å

In case of new λ (assumed λ’ here), angular width decreases by 30%

New angular width = 0.70 (2φ)

2λ’/d = 0.70 × (2λ/d)

∴ λ’ = 4200 Å