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