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. $si{n}^{-1}\frac{n\lambda }{d}$
• B. $co{s}^{-1}\frac{4\lambda }{d}$
• C. $ta{n}^{-1}\frac{d}{4\lambda }$
• D. $co{s}^{-1}\frac{\lambda }{4d}$

Answer 1

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

Here path difference at a point $P$ on the circle is given by$:$

$\Delta x=d\cos \theta$---------------------$\left(1\right)$

for maxima at $P\Delta x=n\lambda$-------------------$\left(2\right)$

from equation $\left(1\right)$ and $\left(2\right)$

$n\lambda =d\cos \theta$

$\Rightarrow \theta {\cos }^{-1}\left(\frac{n\lambda }{d}\right)={\cos }^{-1}\left(\frac{4\lambda }{d}\right)$

hence,

option $\left(B\right)$ is correct answer.