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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _add_deflection(self, x, y, alpha_x, alpha_y, kwargs_lens, idex):
 """ adds the pyhsical deflection angle of a single lens plane to the deflection field :param x: co-moving distance at the deflector plane :param y: co-moving distance at the deflector plane :param alpha_x: physical angle (radian) before the deflector plane :param alpha_y: physical angle (radian) before the deflector plane :param kwargs_lens: lens model parameter kwargs :param idex: index of the lens model to be added :param idex_lens: redshift of the deflector plane :return: updated physical deflection after deflector plane (in a backwards ray-tracing perspective) """

        theta_x, theta_y = self._co_moving2angle(x, y, idex)
        alpha_x_red, alpha_y_red = self._lens_model.alpha(theta_x, theta_y, kwargs_lens, k=self._sorted_redshift_index[idex])
        alpha_x_phys = self._reduced2physical_deflection(alpha_x_red, idex)
        alpha_y_phys = self._reduced2physical_deflection(alpha_y_red, idex)
        alpha_x_new = alpha_x - alpha_x_phys
        alpha_y_new = alpha_y - alpha_y_phys
        return alpha_x_new, alpha_y_new