Question

Interference pattern is observed at '$P$' due to superimposition of two rays coming out from a source '$S$' as shown in the figure. The value of '$l$' for which maxima is obtained at '$P$' is :
($R$ is perfect reflecting surface) :

• A. $l=\frac{2\,n\lambda}{\sqrt{3}-1}$
• B. $l=\frac{\left(2n-1\right)\lambda}{2\left(\sqrt{3}-1\right)}$
• C. $l=\frac{\left(2n-1\right)\lambda\sqrt{3}}{4\left(2-\sqrt{3}\right)}$
• D. $l=\frac{\left(2n-1\right)\lambda}{\sqrt{3}-1}$

Answer 1

Answer: (C)

$x \cos 30^{\circ}=\ell$
$x \frac{\sqrt{3}}{2}=\ell \,\,\,x=\frac{\sqrt{2 \ell}}{\sqrt{3}}$
$\frac{2 \ell}{\sqrt{3}}+\frac{2 \ell}{\sqrt{3}}+\frac{\lambda}{2}-2 \ell=n \lambda$
$2 \ell\left(\frac{2}{\sqrt{3}}-1\right)=(2 n-1) \frac{\lambda}{2}$
$2 \ell(2-\sqrt{3})=\frac{(2 n-1) \lambda \sqrt{3}}{2}$