Employing systematic first-principle calculations to the family of tellurium II-VI compounds such as Hg- and Zn-based semiconductors and their related Zn1-x Hg (x) Te ternary alloys, we have simulated the electronic and optical characteristics incorporating the spin-orbit coupling effect. The salient features such as the band gaps and the optical spectra with a satisfactory adequate approach are computed with the so-called modified Becke-Johnson exchange correlation potential as implemented in the full-potential linearized augmented plane-wave scheme. The theoretical finding surmises that a topological insulating state may be caused with 25% of Zn concentration incorporated in HgTe material. Intriguingly, a band gap is conclusively developed near 0.25 eV in Zn0.25Hg0.75Te alloy. The relevant components like the band structure, optical response functions such as the real and imaginary parts of dielectric function, spectral dependence of optical conductivity, reflectivity spectrum, refractive index, electron energy loss function, and absorption coefficient are established for the bulk Zn1-x Hg (x) Te ternary alloys, while Zn composition spans in the range 0-1. The overall accordance between our results and other theoretical reports as well as experimental realization is fairly good. We infer that the current work may be beneficial for optical emitters/converters in solar cell devices applications.