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 $589.6 \mathrm{nm})$.