The black circle with radius \(R_s\) represents the event horizon of the black hole.

Photons arrive from the right (\(x=+\infty\)

and \(y=b\)) with an impact parameter value \(b\)

that gives a variation of \(\Delta\varphi=\pi\) on entering

the event horizon.

The figure is plotted with Cartesian coordinates \(x=r\cos\varphi\) and \(y=r\sin\varphi\),

considering a black hole of the mass

of the sun \(M\odot\)

that is \(R_s=2 \ 953\ m \), \(b_{crit}=7\ 672.73\ m\), and with \(b=6\ 582\ m\).

The value of \(b\) is obtained by choosing a target value \(r=R_s\) for a variation \(\Delta\varphi\) of \(\pi\)

(Excel spreadsheet) or with the values \(R_s\) et \(\pi\) as input data (Python script).

According to the principle of the inverse return of light, this figure also corresponds

to the emission of photons from the event horizon of the black hole (coordinates \(R_s\) and \(\pi\)) with an impact parameter \(b=6\ 582\ m\).

For a black hole with a different mass \(M\), the plots are kept by applying the scaling factor

\(\frac{M}{M\odot}\).