In this paper, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss–Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter [Formula: see text] and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss–Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the [Formula: see text]. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of non-linear electrodynamics (NLED), plasma and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

In this study, we probe the weak lensing by a Reissner–Nordström black hole corrected by bounce parameter in plasma and dark matter mediums. For this, the optical geometry and the Gibbons–Werner approach are utilized to obtain the bending angle in the weak field limitations. We examine that the impact of these mediums increases the black hole’s bending angle. In addition, we graphically study the deflection angle of light with respect to the impact parameter and examine that the bounce parameter directly affects the angle. Further, we compute the Hawking radiation via a topological method involving two invariants and verify our obtained result with the standard method of calculating the Hawking temperature. In addition, we compute the greybody factor’s bound of the black hole. Moreover, we analyze the bound graphically and observe that the bound shows convergent behavior. We also study that our attained results reduce the results of the Reissner–Nordström and Schwarzschild black holes by reducing the parameters. Finally, we probe how the bounce parameter affected the shadow radius and compared it to the shadow produced if the black hole is immersed in plasma. It is revealed that the rate at which the shadow radius changes with respect to r easily tends to zero under the effect of the bounce parameter, while the plasma merely increases the shadow radius.

In this work, we examine the deflection angle of black hole in effective loop quantum gravity in non-plasma medium via the geometrical technique of Gibbons and Werner in weak field limits. For this, we attain the optical metric and calculate the Gaussian optical curvature and then we apply the Gauss-Bonnet theorem. We also study the influence of the plasma and dark matter mediums on the deflection angle. Further, we obtain the deflection angle by using Keeton and Petters method. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we discuss the graphical behaviour of the bending angle and bounds on the greybody factor. We also examine that the results obtained for the black hole in effective loop quantum gravity are reduces to the Schwarzschild black hole solutions when dimensionless non-negative parameter $A_{\lambda}=0$.