Question

Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda .$ The separation between them is $2\lambda .$ The light is collected on a screen placed at a distance $D>>\lambda$ from the slit $S_1$ as shown. The minimum distance, so that intensity at $P$ is equal to the intensity at $O$

• A. $\sqrt{2}D$
• B. $\sqrt{3}D$
• C. $\sqrt{8}D$
• D. $\sqrt{5}D$

Answer 1

Answer: (B)

Path difference between the light waves form $S_{1}and{S}_2,$ reaching at $P$ is,
$=2\lambda cos\theta$

Since, there is a bright maximum at $O$ . Thus for maximum at $P,$
$2\lambda cos\theta =n\lambda$
For $x$ to be minimum $n=1$
$cos\theta =\frac{1}{2}\Rightarrow \theta =60^{\circ }$
$\therefore x=Dtan60^{\circ }=\sqrt{3}D$