Use Huygens's principle to explain the formation of diffraction p… - Vidyadip

Question

Use Huygens'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 the slit is made double the original width, how would this affect the size and intensity of the central diffraction band?

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Answer

Explanation:
As per Huygen's Principle
Net effect at any point = sum total of contribution 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 $\mathrm{SM}-\mathrm{SM}_1=\lambda / 2$ Phase difference between each wavelet from $\mathrm{SS}_1$ and corresponding wavelet from $\mathrm{SS}_2=\lambda / 2$ Hence, M would be a minima. All such points (path difference $=\mathrm{n} \lambda / 2$ ) are also minima. Similarly, all points, for which path difference $=(2 n+1) \lambda / 2$, are maxima but with decreasing intensity. From the figure

Half angular width of central maxima= $\lambda$/a $\therefore$, Size of central maxima will be reduced to half and intensity of central maxima will be four times.

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