Question

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. ${\tan }^{-1}\frac{4\lambda }{d}$
• D. ${\cos }^{-1}\frac{\lambda }{4d}$

Answer 1

The correct option is B ${\cos }^{-1}\frac{4\lambda }{d}$

Path different at a point P on a circle is given by $\Delta x=d\cos \theta \to \left(i\right)$

for maxima at P, $\Delta x=n\lambda \to \left(ii\right)$

$n\lambda =d\cos \theta ,$ from (i) & (ii)

[B]

$\begin{array}{c}\theta ={\cos }^{-}\left(\frac{n\lambda }{d}\right),Putn=4\\ \theta ={\cos }^{-}\left(\frac{4\lambda }{d}\right)\end{array}$