Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 338 / 2 / a / iii

From the slit profile, the spectral resolving power obeys $R=\lambda q/p$. Substitute into the preceding optical-invariant relation:The slit-image width cancels. Although $q$ is a detector length per unit wavelength, $\lambda q$ is a detector length, so this expression for $L$ has units of length, as does $R\theta D$.