question_answer

Two coherent sources separated by distance\[d\]are radiating in phase having wavelengthl. 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)            \[{{\cos }^{-1}}\frac{\lambda }{4d}\]

Correct Answer: B

Solution :

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