Final answer:
The frequency of light observed from a mirror moving towards an observer at speed v undergoes a Doppler shift, perceived as if the image in the mirror was approaching at speed 2v/(1+v²/c²). Relativistic Doppler effect formulas are used since light's speed is invariant, unlike the classical formula used for sound.
Step-by-step explanation:
The Doppler shift of light plays a crucial role when discussing relative motion between a source and an observer. When a mirror is moving towards an observer with a speed v, light reflected from it experiences a Doppler shift. In the context of a mirror approaching an observer at speed v, the frequency of the light reflected directly back would be observed as if the source (the image in the mirror) itself were approaching the observer at a speed 2v/(1+v²/c²). This happens because the relativistic effects, which include the time dilation and Lorentz contraction, contribute to the observed frequency.
The classical formula for the observed frequency (fo) at speeds less than the speed of sound is fo = fs (-us), where us is the speed of the source. However, for light, we consider that the speed of light (c) is constant and the Doppler shift formulas are modified to take into account relativistic effects. Thus, the observed frequency for light differs from the non-relativistic Doppler shift observed in sound waves. At relativistic speeds, the frequency shift formula incorporates the relativistic Doppler effect, which accounts for the speed of light's invariance.