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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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