One application of the Cosmological Gravitational Lensing in General Relativity is the measurement of the Hubble constant H_0 using the time delay Delta t between multiple images of lensed quasars. This method has already been applied, obtaining a value of H_0 compatible with that obtained from the SNe 1A, but non compatible with that obtained studying the anisotropies of the CMB. This difference could be a statistical fluctuation or an indication of new physics beyond the Standard Model of Cosmology, so it desirable to improve the precision of the measurements. At the current technological capabilities it is possible to obtain H_0 to a percent level uncertainty, so a more accurate theoretical model could be necessary in order to increase the precision about the determination of H_0. The actual formula which relates Delta t with H_0 is approximated; in this paper we expose a proposal to go beyond the previous analysis and, within the context of a new model, we obtain a more precise formula than that present in the Literature.

We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom of the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to arbitrary angles of the standard one, which is valid at small angles. This could therefore result in a useful tool in view of softening the known discrepancy between the various estimates of the Hubble constant. As an aside, two interesting consequences of our proposal for time delay are discussed: the existence of a constraint on the gravitational potential generated by the lens and a formula for the mass of the lens in the case of central potential.