Consider a smooth positively curved ovaloid \(M^ n\) in Euclidean \((n+1)\)-space and a point 0 in the interior of \(M^ n\). The caustic of the system \(\{M^ n,0\}\) is defined as the envelope of the light rays emanating from 0 after reflection on the `mirror' \(M^ n\). This caustic can be considered as the focal set of some hypersurface which is called the orthotomic of the pair \(\{M^ n,0\}\). The orthotomic can be obtained by a similarity from the pedal of \(M^ n\) with respect to 0. Using this relation the authors present a pinching condition on the principal curvatures of \(M^ n\) which ensures that there are many centers 0 for which the caustic of \(\{M^ n,0\}\) lies entirely in the interior of \(M^ n\). The precise conditions are as follows: Assume the principal curvatures of \(M^ n\) to be ordered by \(k_ 1\geq...\geq k_ n>0.\) Suppose \(\max_{M}k1\). Then for every 0 in the interior of the parallel ovaloid to \(M^ n\) along the interior normal at a distance 3/(4 \(\min_{K} k)\) \((n=1)\) resp. \(1/((- 1+\sqrt{5})\min_{M}k_ n)\) \((n>1)\), the caustic of \(\{M^ n,0\}\) has the desired property. In addition to this a simple proof is given for the fact that for every choice of 0 in the interior of \(M^ n\) the caustic of \(\{M^ n,0\}\) has non-empty intersection with the interior of \(M^ n\) [see also \textit{J. W. Bruce, P. J. Giblin} and \textit{C. G. Gibson}, Topology 21, 179-199 (1982; Zbl 0494.58010)].