Suppose that you have a reflection diffraction grating with n=140 lines per millimeter. Light from a sodium lamp passes through the grating and is diffracted onto a distant screen. How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)?
maxima for reflection diffraction grating: sinθ=(mλ)/d where m=2 in this instance
Rayleigh's resolution criterion: sinθ=1.22*(λ/d)
d=distance between slits
The Attempt at a Solution
m=2 and d is the unknown. I tried setting the above equations equal to each other, eliminating sinθ, but I couldn't get any further because I don't know which λ to use since we are trying to separate two different wavelengths.