First, we use the relationship between the spacing of the openings, the wavelength of light, the order of the maxima or minima and the angle of diffraction which is:
d*sinθ = nλ, where d is the spacing, θ is the angle, n is the order and λ is the wavelength. We will use the wavelength in mm so that we may obtain the spacing in mm (510 x 10⁻⁶ mm). Solving for d,
d = (1)(510 x 10⁻⁶) / sin(12)
d = 2.45 x 10⁻³ mm
Using this, we may calculate openings per mm,
1 / 2.45 x 10⁻³
= 408 lines per mm.