Answer
$1.82\;\rm \mu m$
Work Step by Step
We know, in a reflection grating, that the angle of a bright fringe is given by
$$d\sin\theta_m=m\lambda$$
So, the first-order diffraction angle is at $m=1$, and hence,
$$d\sin\theta_1= \lambda$$
Thus, the spacing of the melanin rods in the feather is then given by
$$d=\dfrac{\lambda}{\sin\theta_1}$$
Plugging the known;
$$d=\dfrac{470}{\sin15^\circ}=1816\;\rm nm$$
$$d=\color{red}{\bf 1.82}\;\rm \mu m$$
