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.

Explanation

Explanation , As per Huygen.s Principle , net Effect at any point = Sum of total of contrubution of all wavelets with proper phase difference.

At the central point (O) contribution from each half in `SS_(1)` is in phase with that from the corresponding part in `SS_(2)`. Hence, O is a maxima.

At the point M where `M-S_(1)M=lambda//2`
Phase difference between each wavelet from `SS_(1)` and corresponding wavelet from `SS_(2)=lambda//2`
Hence, M would be a minima,
All such points (path difference `=nlambda//2`) are also minima .
Similarly , all points, for which path difference `=(2n+1)lambda//2`, are in maxima but with decreasing intensity.
From the figure,
Half angular width of central maxima `=lambda//a`
`:.` 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.