Wave Division Multiplexer

A telecommunications engineer is trying to use a transmission grating to make a “Wavelength Division Multiplexer” (WDM), a device that takes a laser beam with several closely spaced wavelengths (each used to transmit a different message), and directs each of them to its own fiber-optic channel:

Assume the collimated laser beam after the initial fiber optic has an average wavelength of 1500 nanometers, and a width of 0.5 mm. This beam is incident upon a grating of width 2-mm which has 450 lines/mm, each with a width of 200 nanometers. The fiber-optics channels are situated to receive light from the first-order interference maxima.

What is R, the distance between the grating and the fiber-optic channels, if the separation between the channels (Δs = 0.5 mm) corresponds to a difference in wavelengths, Δλ = 10 nanometers?

R = cm