We have observed specular reflection and multiple bounces of a beam of
laser-cooled caesium atoms from a magnetostatic mirror consisting of
an array of rare-earth permanent magnets. Using a time-of-flight absor
ption technique, the reflection coefficient of the mirror for caesium
6(2)S(1/2), F = 4 atoms pumped toward the m = +4 state is determined t
o be (100 +/- 2)%. For a beam of unpolarized atoms the reflectivity is
found to be unexpectedly high, (90 +/- 5)%, which is attributed to co
ntributions from atoms in m = 0, -1, -2 states which are reflected at
high magnetic fields close to the surface of the mirror as a result of
the quadratic Zeeman effect.