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  • Derive an expression for path difference in Youngs doubleslit experiment and obtain the conditions for constructive and destructive interference

Derive an expression for path difference in Youngs doubleslit experiment and obtain the conditions for constructive and destructive interference

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d<<D

For constructive interference

S_{2}P-S_{1}P=n\lambda

\left [ D^{2} +\left ( x+\frac{d}{2} \right )^{2}\right ]-\left [ D^{2} +\left ( x-\frac{d}{2} \right )^{2}\right ]

=S_{2}P^{2}-S_{1}P^{2}

\Rightarrow S_{2}P^{2}-S_{1}P^{2}=xd

(S_{2}P-S_{1}P)(S_{2}P+S_{1}P)=xd

S_{2}P-S_{1}P=\frac{xd}{D}\; \; \; \; \; \; \; \; (d<<D)

\therefore \frac{xd}{D}=n\lambda

or x_{n}=\frac{n\lambda D}{d}\; \; \; \; (n=o,\pm 1,\pm 2)

for destructive interference

\frac{xd}{D}=\left ( n+\frac{1}{2} \right )\lambda                 (n=o,\pm 1,\pm 2)

Posted by

Safeer PP

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