  We investigate the effects of the relativistic movement of an optical medium
on the conditions of constructive and destructive interference, reflection and
transmission pattern, and performance of spectroscopes. First, we consider the
case of two beams reflected from a relativistically moving thin film and derive
the conditions of constructive and destructive interference. Then we broaden
the idea to multiple beam interference and formulate a new modified equation of
reflection and transmission pattern of light from a relativistically moving
plane parallel dielectric film. Finally, we determine the new effective
resolving power of a Fabry-Perot spectroscope, which has a moving dielectric
medium in its etalon. Here, we consider the case where the optical media move
parallel to the plane of incidence of light. Throughout this paper, we use
basic Lorentz transformation of space and time co-ordinates and electromagnetic
fields to conduct these investigations. This paper can strongly motivate
undergraduate physics students to associate the concepts of special relativity
and optical interference.
