Answer
$5.0\mu m $
Work Step by Step
From the given graph, we see that the first minimum happens when $\theta=5^{\circ}$. We are given a wavelength of $0.440\mu m$
We can now use equation (36-3) with $m=1$ to solve for the slit width;
$a \sin \theta = m \lambda $ where $m=1,2,3,....$ (minima) (36-3)
Therefore;
$a = m \lambda/ \sin \theta $
$a = 1* 0.440\mu m/ \sin 5.0^{\circ} $
$a = 5.0\mu m $
