Past exam of the physics 2 paper of the University of Oxford / 2021 resit / 9 / c

Because optical dispersion makes the refractive index depend on wavelength, no single angle of incidence makes every component of white light travel parallel to the base. Choose the supplied central visible wavelength $535\mathrm{nm}$, with $n_0=1.86$, as the design component. Snell's law givesKeep this angle of incidence fixed for all colours. The other components haveSubstitution givesAll three emerge: the largest value of $n\sin r_2$ is about $0.9323<1$. The angular spread between the extreme supplied wavelengths isThe respective deviations are $72.988^{\circ }$, $63.376^{\circ }$ and $60.398^{\circ }$. Applying the symmetric formula independently to the two extreme refractive indices would instead give $72.221^{\circ }-60.344^{\circ }=11.877^{\circ }$; that compares differently oriented optical prisms, not the emerging components of one fixed white-light beam. It can be a rough approximation but misses the stated fixed-incidence geometry. The supplied $370\mathrm{nm}$ value is near ultraviolet, so the computed spread refers to the entire supplied band, not a universally defined visible-white spectrum.