Answer
(a) $12\mu m$
(b) decrease
Work Step by Step
(a) We can determine the width of the slit as follows:
$W=L(\frac{\lambda}{\Delta y})$
We plug in the known values to obtain:
$W=\frac{(2.3m)(610\times 10^{-9}m)}{0.12m}$
$W=11691.66\times 10^{-9}m=12\mu m$
(b) We know that
$\Delta y=\frac{L\lambda}{W}$
This equation shows that if the width of the slit increases then the linear distance between the first and second dark fringe decreases.
