  We study the set of trapped photons outside the event horizon of
Schwarzschild-Tangherlini black holes in dimension $d\geq4$. We prove that the
only trapped photons are those with constant Boyer-Lindquist coordinate radius.
We then identify the set of trapped photons as a submanifold of the tangent
bundle of the spacetime, and prove that this submanifold has topology $T^1
S^{n-1}\times \mathbb{R}^2$, as suggested in [7].
