Light is sent through a single slit of width w = 0.52 mm. on a screen, which is l = 1.6 m from the slit, the width of the central maximum is d = 4.42 mm.

Randomized variables
w = 0.42 mm
L = 1/9 m
D = 4.8 mm

The angle of the first dark fringe is θdark. Express sin(θdark) in terms of the wavelength of the light λ and w.