  We consider the projection of null geodesics of the Schwarzschild-Tangherlini
metric in n+1 dimensions to the space of orbits of the static Killing vector
where the motion of a given light ray is seen to lie in a plane. The projected
curves coincide with the unparametrised geodesics of optical 2-metrics and can
be equally understood as describing the motion of a non-relativistic particle
in a central force. We consider a duality between the projected null curves for
pairs of values of n and interpret its mathematical meaning in terms of the
optical 2-metrics. The metrics are not projectively equivalent but the
correspondence can be exposed in terms of a third order differential equation.
We also explore the extension of this notion of duality to the
Reissner-Nordstrom case.
