Question

Two wavelengths of sodium light 590 nm and 596 nm are used, in turn to study the diffraction taking place at a single slit of aperture 2 × 10⁻⁴m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

Answer 1

Given that: Wavelength of the light beam, λ₁ = 590 nm = 5.9 ×10^-7 m

Wavelength of another light beam, λ₂ = 596 nm = 5.96 ×10^-7 m

Distance of the slits from the screen = D = 1.5 m

Distance between the two slits = a = 2 ×10^-4 m

For the first secondary maxima, `sin θ = (3λ_1)/(2a) = x_1/D`

or

`x_1 = (3λ_1D)/(2a) and x_2 = (3λ_2D)/(2a)`

∴ Spacing between the positions of first secondary maxima of two sodium lines `x_1 -x_2 = (3D)/(2a)(λ_2 -λ_1) = 6.75 xx 10^-5m`