1. Tardigrade
  2. Question
  3. Physics
  4. Two coherent point sources S1 and S2 vibrating in phase emit light of wavelength λ . The separation between them is 2λ . The light is collected on a screen placed at a distance D>>λ from the slit S1 as shown. The minimum distance, so that intensity at P is equal to the intensity at O <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-6m7m3xsweufgbyt8.jpg />

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 $O$
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Path difference between the light waves form $S_{1} \, and \, S_{2},$ reaching at $P$ is,
$=2\lambda cos\theta $
Solution
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 $
$\therefore x=D \, tan60^\circ =\sqrt{3}D$