
POLARIZED LIGHT 143
6.4.1 Snell’s Law
When we apply the boundary conditions, we recognize that they must apply along the entire
boundary, which means they are independent of y. Therefore the transverse components of kn
should be constant across the boundary,
kn
1
sin θ
i
= kn
1
sin θ
r
= kn
2
sin θ
t
, (6.43)
with the results that
θ
i
= θ
r
n
1
sin θ
i
= n
2
sin θ
t
. (6.44)
Thus, Snell’s law can be derived directly from the boundary conditions, and specically from
the preservation of nk sin θ across the boundary.
6.4.2 Reflection and Transmission
Equation 6.40 requires that there be no change in the transverse component of E.ForS
polarization, E is completely transverse, and ...