Answer
$d=31\mu m$
Work Step by Step
We can use the given wavelength and half of the given angle ( because we require the angle to be measured from the center to the edge, not from edge to edge) in equation (36-12) to solve for the diameter, d, of the structure producing the diffraction.
$\sin \theta = 1.22 \frac{\lambda}{d}$
$d = 1.22 \frac{\lambda}{\sin \theta}$
$d = 1.22 \frac{550*10^{-9}m}{\sin (2.5^{\circ}/2)}$
$d=31*10^{-6}m$
$d=31\mu m$
