Answer
$3.03\times10^{-5}m $. As suggested, apply the equation for single-slit diffraction, using the thickness of the hair instead of the width of the slit.
Work Step by Step
Use equation 36.3 because the angle is small.
$$y_1=\frac{x \lambda}{a}$$
The distance between the two dark fringes on either side of the central maximum is $5.22 cm = 2y_1$.
$$y_1=\frac{x \lambda}{a}$$
$$a=\frac{x \lambda}{y_1}$$
$$a=\frac{(1.25m) (632.8\times10^{-9}m)}{2.61\times10^{-2}m}=3.03\times10^{-5}m $$
