  The present study examines the gravitational deflection of particles in
curved space-times immersed in perfect fluid in the context of Rastall theory,
applying the Gibbons-Werner useful technique. In its application to integral
areas inside a four-dimensional space-time, the Gauss-Bonnet theorem studies
the computation expression of the deflection angle. The Gibbons-Werner
technique has two limitations in Rastall theory for space-times immersed in
perfect fluid: the integral region is generally infinite and the integral
complicates calculation, particularly for complex space-times and extremely
accurate solutions. An infinite region approach to Gibbons-Werner is proposed
to avoid singularity. For demonstrating the Gibbons-Werner method, we use a
complete Rastall theory framework. It studies black hole solutions like the
dust field, radiation field, quintessence field, cosmological constant field
and phantom field using the Gibbons-Werner approach. Additionally, we check the
deflection angle from these space-times under the influence of plasma.
Furthermore, we compute analytically the influence of a plasma on a black hole
shadow by using a ray-tracing approach. In the Hamiltonian equation, our model
describes the plasma, so the light ray motion equations are independent of the
plasma's velocity. It is assumed that plasma is a dispersive medium,
pressure-less and non-magnetized. We investigate the perfect fluid in Rastall
theory in further depth, where the plasma particle density corresponds to
particle accumulation. The supermassive black hole shadows are explored in the
case when plasma falls radially from infinity onto a black hole.
