But, from the law of reflection, and , so

Trigonometry also yields

It follows from the previous two equations that

Hence, , for all values of .

It can easily be appreciated that a combination of *three*
mutually perpendicular mirrors would reflect a light-ray incident from
*any* direction through . Such a combination of
mirrors is
called a *corner-cube reflector*. Astronauts on the Apollo 11
mission (1969) left a panel of
corner-cube reflectors on the surface of the Moon. These reflectors
have been used ever since to measure the Earth-Moon distance
via laser range finding (basically, a laser beam is fired from
the Earth, reflects off the corner-cube reflectors on the
Moon, and then returns to the Earth. The time of travel of the beam
can easily be converted into the Earth-Moon distance). The Earth-Moon
distance can be measured to within an accuracy of using
this method.