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. $l=\frac{2n\lambda }{\sqrt{3}-1}$
• 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)

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