Question

Use Huygen’s principle to explain the formation of diffraction pattern due to a single slit illuminated by a monochromatic source of light. When the width of slit is made double the original width, how this affect the size and intensity of the central diffraction band?

Answer 1

According to Huygen's principle "The net effect at any point due to a number of wavelets is equal to sum total of contribution of all wavelets with proper phase difference. 

The point O is maxima because contribution from each half of the slit S₁S₂ is in phase, i.e., the path difference is zero. 

At point P 

(i) If S₂P – S₁P = nλ => the point P would be minima. 

(ii) If S₂P - S₁P = (2n + 1)λ/2 => the point would be maxima but with decreasing intensity. The width of central maxima = 2λD/a 

When the width of the slit is made double the original width, then the size of central maxima will be reduced to half and intensity will be four times.