  In this article, we have investigated the equations of motion of the photons
coupled to Weyl tensor by the geometric optics approximation and the
corresponding shadow in a Brane-World black hole spacetime. It is shown that
there exists a double shadow for a black hole since the coupling photons with
different polarization directions propagate along different paths in the
spacetime. Furthermore, we discuss the effects of the metric parameter $\alpha$
related to the cosmological constant, X-cold dark matter parameter $\beta$ and
the coupling parameter $\lambda$ on the umbra (the overlap region of the double
shadow) and the penumbra. We also obtain the finite-distance corrections to the
deflection angle of light in the Brane-World black hole spacetime as the
photons coupled to Weyl tensor by using a recent geometric method.
