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)

Question

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), 4 . 5 cm, 1 . 5 cm, 6 . 0 cm, 3 . 0 cm

MARKS App · Accepted Answer

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 x 2 - x 1 = 4 λ d - 2 λ d = 2 λ d = 6 - 3 = 3 c m Width of central max ⁡ = 2 λ d = 3 c m

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