  In this paper, we mainly aim at highlighting the importance of
(hyper-)elliptic integrals in the study of gravitational effects caused by
strongly gravitating systems. For this, we study the application of elliptic
integrals in calculating the light deflection as it passes a plasmic medium,
surrounding a charged Weyl black hole. To proceed with this, we consider two
specific algebraic ansatzes for the plasmic refractive index, and we
characterize the photon sphere for each of the cases. This will be used further
to calculate the angular diameter of the corresponding black hole shadow. We
show that the complexity of the refractive index expressions, can result in
substantially different types of dependencies of the light behavior on the
spacetime parameters.
