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. ${\cos }^{-1}\left(\frac{\lambda }{4d}\right)$
• B. ${\tan }^{-1}\left(\frac{\lambda }{4d}\right)$
• C. ${\sin }^{-1}\left(\frac{4\lambda }{d}\right)$
• D. ${\cos }^{-1}\left(\frac{4\lambda }{d}\right)$

Answer 1

The correct option is D ${\cos }^{-1}\left(\frac{4\lambda }{d}\right)$


The path difference at $P$ is,

$\Delta x=d\cos \theta$

For intensity to be maximum,

$\Delta x=n\lambda$

$\Rightarrow d\cos \theta =n\lambda$

$\Rightarrow \cos \theta =\frac{n\lambda }{d}$

Given, $n=4$

$\therefore \cos \theta =\frac{4\lambda }{d}$

Angular position of $n=4$

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

Hence, option $\left(\text{D}\right)$ is correct.