  We derive the reflection and refraction laws for an electron spin incident
from a quasi-two-dimensional medium with no spin-orbit interaction on another
with both Rashba and Dresselhaus spin-orbit interaction using only energy
conservation. We obtain the well-known result that for an incident angle, there
can be generally two different refraction angles for refraction into the two
spin eigenstates in the refraction medium, resulting in two different 'spin
refractive indices' and two critical angles for total internal reflection. We
derive expressions for the spin refractive indices, which are not constant for
a given medium but depend on the incident electron's energy. If the effective
mass of an electron in the refraction medium is larger than that in the
incidence medium, then we show that for some incident electron energies and
potential barrier at the interface, the spin refractive index of the incidence
medium can lie between the two spin refractive indices of the refraction
medium, resulting in only one critical angle. In that case, if the incident
angle exceeds that critical angle, then refraction can occur into only one spin
eigenstate in the refraction medium. If the system is engineered to make this
happen, then it will be possible to obtain a very high degree of spin-polarized
injection into the refraction medium. The amplitudes of reflection of the
incident spin into its own spin eigenstate and the orthogonal spin eigenstate
(due to spin flip at the interface), as well as the refraction amplitudes into
the two spin eigenstates in the refraction medium are derived for an incident
electron (with arbitrary spin polarization and incident energy) as a function
of the angle of incidence.
