<p>The study explores a similarity solution for a shock wave in magnetogasdynamics, considering monochromatic radiation and an azimuthal magnetic field within a rotating non-ideal medium. The initial magnetic field and fluid velocities of the ambient medium are supposed to be varying. Similarity solutions are established for power as well as exponential law shock path cases. The numerical solution for case Ia (power law) and case IIa (exponential law) are derived. The flow field behind the shock front gets rarefied in both power and exponential laws, indicating that the parameter of non-idealness and the adiabatic exponent have a declining influence on shock strength with an increase in these parameters. In the power law case, elevation of the rotational parameter enhances the shock strength, whereas in exponential law case, the opposite trend is noted.</p>