\(a \sin \theta=\lambda\)

Here \(\theta=30^{\circ} \Rightarrow \sin \theta=\frac{1}{2}\)

\(\therefore \quad a=2 \lambda\)    ..... \((i)\)

For first secondary maximum, the path difference between extreme waves

\(a \sin \theta=\frac{3}{2} \lambda\) or \((2 \lambda) \sin \theta^{\prime}=\frac{3}{2} \lambda\)  [Using eqn \((i)\)]

or \(\sin \theta^{\prime}=\frac{3}{4} \quad \therefore \theta^{\prime}=\sin ^{-1}\left(\frac{3}{4}\right)\)