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## Homework Statement

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)?

## Homework Equations

maxima for reflection diffraction grating: sinθ=(mλ)/d where m=2 in this instance

Rayleigh's resolution criterion: sinθ=1.22*(λ/d)

Spectrometer: λ=(d/m)*sinθ

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.