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

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

and \(y=b\)) in the same plane.

Each value of the impact parameter \(b\) gives

a different deviation. In dark blue deviation

of \(\pi\over 2\), in light blue deviation of \(\pi\), in green deviation of \(3\pi\over 2\) and in yellow deviation of \(2\pi\) (full revolution).

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 \(b_{\pi\over 2} = 9\ 107\ m\), \(b_{\pi} = 7\ 910\ m\), \(b_{3\pi\over 2} = 7\ 720\ m\) and \(b_{2\pi} = 7\ 682\ m\).

Each value of \(b\) is obtained by choosing the value of the final variation \(\Delta\varphi\) = deviation + \(\pi\) (target value in Excel spreadsheet or input data in Python script).

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

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

3D illustration

The black sphere is the event horizon

of the black hole, with radius \(R_s\)

and the light yellow sphere is the sphere

of photons, with radius\(\frac{3}{2}R_s\).

The figure is plotted in three dimensions

(90° and 360° deviations in an xy plane,

180° deviation in an xz plane

and 270° deviation in a yz plane).