Q. Two coherent sources separated by distance $d$ are radiating in phase having wavelength $\lambda$. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of $n = 4$ interference maxima is given as
A) $\sin^{- 1}\frac{n\lambda}{d}$
B) $\cos^{- 1}\frac{4\lambda}{d}$
C) $\tan^{- 1}\frac{d}{4\lambda}$
D) $\cos^{- 1}\frac{\lambda}{4d}$
Explanation
(b) Here path difference at a point $P$ on the circle is given by
$\Delta x = d\cos\theta$ …(i)
For maxima at $P$
$\Delta x = n\lambda$ …(ii)
From equation (i) and (ii)
$n\lambda = d\cos\theta \Rightarrow \theta = \cos^{- 1}{\left( \frac{n\lambda}{d} \right) = \cos^{- 1}\left( \frac{4\lambda}{d} \right)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.