A single slit of width b is illuminated by a coherent monochromatic light of wavelength λ . If the second and fourth minima in the diffraction pattern at a distance 1 cm from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum? (i.e. distance between first minimum on either side of the central maximum)

Step-by-step solution

For secondary minima d sin ⁡ θ = n λ sin ⁡ θ = n λ d For second minima n = 2 sin ⁡ θ = 2 λ d = tan ⁡ θ 1 = x 1 D For fourth minima n = 4 sin ⁡ θ 2 = 4 λ d = x 2 D Distance between both minima is x 2 - x 1 = 4 λ d - 2 λ d = 2 λ d = 6 - 3 =3   cm Width of central maxima, = 2 λ d = 3   c m