Explanation

(c) $I = I_{\max}{\cos^{2}\ }\left( \frac{\phi}{2} \right)$
$\therefore\frac{I_{\max}}{4} = I_{\max}\cos^{2}\frac{\phi}{2}$
$\cos{\frac{\phi}{2} = \frac{1}{2}}$
Or $\frac{\phi}{2} = \frac{\pi}{3}$
$\therefore\ \phi = \frac{2\pi}{3} = \left( \frac{2\pi}{\lambda} \right)\ .\ \Delta x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
Where $\ \Delta x = d\sin\theta$
Substituting in Eq. (i) we get,
$\sin\theta = \frac{\lambda}{3d}$
Or $\ \theta = \sin^{- 1}\left( \frac{\lambda}{3d} \right)$