Sodium light of wavelengths 650   nm and 655   nm is used to study diffraction at a single slit of aperture 0 . 5   mm . The distance between the slit and the screen is 2 . 0   m . The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _____ × 10 - 5   m

Step-by-step solution

The condition for maxima in diffraction is, b sin θ = 2 n + 1 λ 2 . For the first maxima n = 1 . Therefore, b sin θ = 3 λ 2 ⇒ sin θ = 3 λ 2 b = y D y = 3 λ D 2 b Now the difference between the positions of the maxima will be, y 1 - y 2 = 3 D 2 b λ 1 - λ 2 ⇒ y 1 - y 2 = 3 × 2 2 × 5 × 10 - 4 × 655 - 650 × 10 - 9 = 3 × 10 - 5   m