Past exam of the physics 2 paper of the University of Oxford / 2018 / 10 / iv / Solution

Assume normal dispersion, so shorter visible wavelengths have larger refractive indices. At fixed external angle $\theta$, the relevant criticality parameter iswhich increases with $n$ on this route. Thus shorter-wavelength blue light is totally reflected at B and reaches C, while longer-wavelength red light can transmit through B; green lies at the critical threshold. The prism separates the routes by wavelength near the green cutoff.

The totally reflected rays emerging from C have the same external deviation $180^{\circ }-2\alpha +2\theta$ despite their different refractive indices; their exit positions can differ. Red light also has a partially reflected component by the Fresnel equations, so C is not a mathematically perfect colour cutoff. The observation concerns total versus partial reflection, with the transmitted B rays spread by wavelength. Anomalous dispersion, if present, would require the actual $n(\lambda )$ instead of the normal ordering assumed here.