$Pb_{1-x}$ $Cd_{x}$ $I_2$ (x=0.0, 0.2, 0.5, 0.7, 0.9, 1.0) single crystals were grown by using Bridgman method and their structural and optical properties were investigated from the measurement of X-ray diffraction, optical absorption and photoluminescence. As-grown single crystals have hexagonal closed packed layered structure. The values of lattice constant c decrease with increasing composition x. Direct and indirect transition optical energy band gaps are calculated from optical absorption spectra measured at room temperature. They increase exponentially from 2.3eV to 3.2 eV with increasing composition x. The energies of photoluminescence peak due to donor bound exciton measured at 6K increase with increasing composition . However, the peak energies of donor-acceptor pair (DAP) are independent of the optical energy band gaps of $Pb_{1-x}$/$Cd_{x}$ $I_2$ single crystals.