Problem 5.144

A spectrograph's trihedral prism is manufactured from glass whose refractive index varies with wavelength as \(n=A+B / \lambda^{2}\) where \(A\) and \(B\) are constants, with \(B\) being equal to \(0.010 \mu \mathrm{m}^{2}\). Making use of the formula from the foregoing problem, find: (a) how the resolving power of the prism depends on \(\lambda\); calculate the value of \(\lambda / \delta \lambda\) in the vicinity of \(\lambda_{1}=434 \mathrm{nm}\) and \(\lambda_{2}=656 \mathrm{nm}\) if the width of the prism's base is \(b=5.0 \mathrm{~cm} ;\) (b) the width of the prism's base capable of resolving the yellow doublet of sodium \((589.0\) and \(589.6 \mathrm{nm})\).