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N
perp N L
L
θ L
G
G
sin
θ
η L
η T
T
θ T
N
cos
θ
T
T
Figure 6.6. The angle of incidence θ L and the angle of transmission θ T are related by
Snell's law, given in Equation (6.91). The refraction vector T is expressed in terms of its
components parallel and perpendicular to the normal vector N .
Replacing
sin θ L with
2
2
(
NL finally yields
)
2
1
cos
θ
=
1
L
η
η
2
η
L
L
(
)
L
T
=
NL
1
1
NL
2
NL .
(6.96)
2
η
η
η
T
T
T
L T , then it is possible for the quantity inside the radical in Equation
(6.96) to be negative. This happens when light inside a medium having a higher
index of refraction makes a wide angle of incidence with the surface leading to a
medium having a lower index of refraction. Specifically, Equation (6.96) is only
valid when sin θηη
If ηη
>
L T L . If the quantity inside the radical is negative, a phe-
nomenon known as total internal reflection occurs. This means that light is not
refracted, but is actually reflected inside the medium using Equation (6.90).
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