$r\gg b$. One may linearize consistently in several small parameters, but the most frequent is the linearization in $M$ which is always the smallest one. However, Darwin’s exact solution (\[theta(r)\]) is often better approximated by an ad hoc formula rather than by applying some general approximation scheme; this is mainly true at low radii where the weak-field linearizations give too “weak" result (we will discuss this issue in more detail elsewhere [@Semerak-15]). A good example is the formula provided by Beloborodov [@Beloborodov-02] which is often used in the accretion-disc community. Another usable possibility is to approximate the photon meridional-plane trajectory by a suitably adjusted hyperbola. Choosing correctly the asymptotic angle $\theta_\infty$ along which the photon approaches radial infinity, such a hyperbola may be the best approximation at large distances, though close to a horizon it is again bent less than the actual relativistic trajectory. Given the symmetry of our radiation field, both these options can only be used for photons that make less than a $90^\circ$ change in direction, however. Still another possibility is to use a pseudo-Newtonian approach and simulate the Schwarzschild field by a suitably modified Newtonian-type potential. Various forms of such a potential have been suggested, starting 