CBSE Class 12 · 2012 · Wave OpticsShort Answer

$\text{Formation of the pattern:}$ by Huygens' principle every point of the wavefront at the slit $AB$ (width $a$) acts as a source of secondary wavelets. Wavelets travelling straight ($\theta =0$) arrive in phase at the centre $O$ and give the bright central maximum.
For a direction $\theta$, the path difference between wavelets from the two edges is $a\sin \theta$. A minimum occurs when the slit can be divided into pairs of halves that cancel:

and secondary maxima occur approximately at

This produces a bright central band flanked by alternate dark and weak bright bands (see intensity plot).
$\text{Effect of doubling the width:}$ the angular half-width of the central band is $\theta \approx \frac{\lambda }{a}$, so its linear width $\propto \frac{1}{a}$. Doubling $a$ therefore $\text{halves}$ the width of the central band. Since twice the width of slit lets through twice the amplitude into half the area, the central intensity becomes about $\text{four times}$ as great.