Question

A parallel beam of monochromatic light falls normally on a narrow slit of width'a' to produce a diffraction pattern on the screen placed parallel to the plane of the slit. Use Huygens principle to explain that 

(i) the central bright maxima is twice as wide as the other maxima. 

(ii) the intensity falls as we move to successive maxima away from the centre on either side.

Answer 1

Explanation: As per Huygens' Principle, net effect at any point = Sum total of contribution of all wavelets with proper phase difference.

At the central point (O) the contribution from each half in SS₁ is in phase with that from the corresponding part in SS₂ .

Hence, O is a maxima.

At the point M where S₂M - S₁M = λ/2 Phase difference between each wavelet from SS₁ and corresponding wavelet from SS ₂ = λ/2

Hence, M would be a minima.

All such points (path difference = n λ/2) are also minima.

Similarly, all points, for which path difference = (2n +1)λ/2, are maxima but with decreasing intensity.

From the figure,

Half angular width of central maxima = λ/a

.'. The size of central maxima will be reduced to half and intensity of central maxima will be four times if slit is made double the original width.