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In this paper, we use the Gauss Bonnet theorem to obtain the deflection angleby the photons coupled to Weyl tensor in a Schwarzschild black hole andSchwarzschild-like black hole in bumblebee gravity in the weak limitapproximation. To do so, we first calculate the corresponding optical metrics,and then we find the Gaussian curvature to use in Gauss-Bonnet theorem, whichis first done by Gibbons and Werner. Hence, in the leading order terms we showthe deflection angle, that is affected by the coupling between the photon andWeyl tensor, and there is a deviation from the deflecting angle as comparedwith Schwarzschild black hole with Schwarzschild-like black hole in bumblebeegravity. Moreover, we investigate the deflection angle by Einstein-Rosen typewormhole in Weyl gravity and in bumblebee gravity. Interestingly, thedeflection angle by Einstein-Rosen type wormhole in bumblebee gravity is foundas larger than the the deflection angle by Einstein-Rosen type wormhole in Weylgravity.

Gravitational Lensing Under the Effect of Weyl and Bumblebee Gravities: Applications of Gauss-Bonnet Theorem