question_answer

Two coherent sources separated by distance d are radiating in phase having wavelength X. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position 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 :

[b] Path difference,   \[\Delta x={{S}_{1}}P-{{S}_{2}}P=d\cos \,\theta \]   \[\therefore \,d\cos \theta =4\lambda \] or\[\cos \theta =(4\lambda /d)\]