  Virbhadra and Ellis have proposed an exact equation (referred to as VE
equation) for the gravitational lens in a static and spherically symmetric
spacetime [Phys. Rev. D 62,084003 (2000)], whereas an improved equation
(referred to as BTOA equation) has been derived by Bozza [Phys. Rev. D 78,
103005 (2008)] and later by Takizawa, Ono and Asada [Phys. Rev. D, 102, 064060
(2020)]. VE and BTOA equations seem to be very different from each other. The
present paper shows that there exists an unphysical branch in VE equation.
Consequently, VE equation can be reduced by removing the unphysical branch. The
reduced version of VE equation is found to be the same as BTOA equation when a
suitable transformation is made between the deflection angles defined
differently in the two formulations. An explicit expression of the
transformation is found. We also argue possible numerical errors when the
transformation between the deflection angles is ignored.
