In this work, we explore possible topological insulating state in bismuth doped with arsenic Bi1−xAsx. Infrared and magneto‐optical spectroscopy are employed to probe the electrodynamic response of Bi1−xAsx with x = 0.01, as well as topological insulator Bi1−xSbx with x = 0.20. The spectra are reported in magnetic fields up to 18 T, and at temperatures between 10 and 300 K. The results indicate strong sensitivity of optical properties to these external stimuli in both Bi1−xAsx and Bi1−xSbx, but also some differences introduced by arsenic doping. Most notably, the field dependence of cyclotron resonance in Bi1−xAsx implies that it is due to bulk carriers, as opposed to surface carriers in Bi1−xSbx.