If a mirror were moving away from you at half the speed of light, the behavior of your reflection would still follow the basic principles of reflection. However, due to the relativistic effects of the mirror's motion, you would observe some noticeable changes.
According to the theory of relativity, when objects move at significant fractions of the speed of light, several relativistic effects come into play. One of these effects is known as the relativistic Doppler effect. It causes a shift in the frequency of light as observed by an observer moving relative to the source.
In the scenario you described, as the mirror is moving away from you at half the speed of light, the light reflecting off the mirror's surface would experience a redshift. The redshift occurs because the relative motion of the mirror causes the wavelength of the reflected light to stretch, resulting in a decrease in observed frequency.
Consequently, when you observe your reflection in the mirror, the reflected light would appear "redder" than it would if the mirror were stationary or moving at a much slower speed. This is similar to how the pitch of sound changes when a moving object approaches or recedes from an observer.
It's important to note that at half the speed of light, the relativistic effects are noticeable but not extreme. However, as the speed of the mirror approaches the speed of light, relativistic effects become more pronounced, leading to significant changes in how the reflection would appear.