The two most important wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating at 500 lines per mm, and the light is observed on a screen 1.50 m behind the grating.
For 486nm:
Θ = arcsin(m*lambda/(d)) = 0.245457358545082 rad
y (exact) = D*tan(Θ) = 0.375763012193676 m
For 656nm:
Θ = arcsin(m*lambda/(d)) = 0.334185670738279 rad
y (exact) = D*tan(Θ) = 0.520812535442466 m
Distance between high beam = 0.14504952324879 m
d= 1 mm/500 lines. Be sure to convert everything to the same units (mm or nm or m) dsin(theta)=m (lambda). Rearrange the equation to solve for theta. (theta)=arcsine m (lambda)/d. y=Ltan (theta). Solve for the two wavelengths, then find the difference to get the answer.