Consider an infrared grating with 840 lines per millimeter a

Consider an infrared grating with 84.0 lines per millimeter and 15.0 mm of illuminated area. Calculate the first-order resolution of this grating. How far apart (in cm^-1) must two lines centered at 1200 cm^-1 be if they are to be resolved?

Solution

the first order resolution of the grating is,

       R = mM = [1][84 lines/mm][15 mm] = 1260

the resolution distance is,

    y/d = 1.22[lambda/d]

       y = 1.22[(2*pi/k)]

       = 1.22*[(2*pi/1200)]

      = 0.00638467 cm

   1/y = 156.6 cm^-1