Graphics Reference
In-Depth Information
n
→
θ
1
θ
1
Refractive index η
1
Refractive index η
2
θ
2
Figure 1.8
Reflection and refraction of light at the interface between two media. The angle of inci-
dence is the angle of reflection, and the amount of reflected light is the Fresnel reflectance.
The angle of refraction is governed by Snell's law. Both depend on the refractive indices
of the media.
face of water is another example. The boundary is between the surface and the
air, or whatever medium lies above the surface.
The ratio of the reflected flux to the incident flux as derived from Maxwell's
equations is called the
Fresnel reflectance
. In terms of the incoming angle
θ
1
and
the angle of refraction
θ
2
, the Fresnel reflectance
F
r
is given by
sin
2
tan
2
1
2
(
θ
1
−
θ
2
)
(
θ
1
−
θ
2
)
F
r
=
)
+
.
(1.14)
sin
2
tan
2
(
θ
+
θ
)
(
θ
+
θ
1
2
1
2
Snell's law provides the relationship between the angle of incidence and the angle
of refraction:
η
1
sin
θ
1
=
η
2
sin
θ
2
(1.15)
where
η
2
are the refractive indexes of the outside and inside media, re-
spectively (
Figure 1.8
)
. The complement of the Fresnel reflectance
η
1
and
F
t
=
1
−
F
r
(1.16)
is the
Fresnel transmittance
, which is the ratio of transmitted flux to the incident
flux at a surface.
The Fresnel reflectance is defined for purely specular reflection, but it can be
extended to other surfaces by averaging the Fresnel reflection from all incoming
directions. If
η
=
η
1
/
η
2
is the ratio of the refractive indices, the
diffuse Fresnel
