A common method for finding wavelength is to use diffraction grating. The relationship between wavelength λ and the angle of max intensity θ for first order interference is λ = d*sinθ where d is the spacing between lines on the grating, which is the inverse of the grating line density N (d=1/N). This data was taken on a laser of unknown wavelength:
N = 602 ± 2 lines/mm
θ = 22.4°± 0.4°
Δλ = √[ ( Δd*∂λ/(∂d) )2 + Δθ*∂λ/(∂θ) )2 ]
σx = (w/2)/√6 ~ pdf uncertainty for analog measurements // I wouldn't think this is needed, since it's for measurements with calibration uncertainty...right?
The Attempt at a Solution
Well, the above equation is part of the attempt.
The partial with respect to distance (d) is sinθ.
The partial with respect to θ is d*cosθ.
∴ Δλ = √[ ( 2*sin(22.4°) )2 + 0.4*cos(22.4°)/602 )2 ] = 0.762
λ = 6.33 ± 0.762 mm