Question

A slit of width 'd' is illuminated by light of wavelength 6000 A. For what value of d will i) the first maximum fall at an angle of 30°. ii) First minimum fall at an angle of 30°.

Answer 1

First minimum (dark fringe) at d sin θ = n λ , where n = 1
so sin θ = λ / d
d = 6000 * 10⁻¹⁰ m * 2 = 1.2 μ meter

first maximum (after central bright region and first dark fringe) falls at
sinθ = (n+1/2) λ/d , where n = 1
d = 3/2 * λ / sinθ = 1.8 μm