The following table gives data about the single slit diffraction experiment:

The following table gives data about the single slit diffraction experiment:

Find the ratio of the widths of the slits used in the two cases. Would the ratio of the half angular widths of the first secondary maxima, in the two cases, be also equal to q ?

Let d and d’ be the width of the slits in the two cases.
$\theta $ = $\lambda $/d and q$\theta $ = p$\lambda $/d’
d/d’ = q/p
Yes, this ratio would also be equal to q.