Page 257 - Modern Optical Engineering The Design of Optical Systems

Chapter
11

Optical Coatings

11.1 Dielectric Reflection and Interference
Filters
The portion of the light reflected (Fresnel reflection) from the surface
of an ordinary dielectric material (such as glass) is given by

2
1 sin (I I′) tan (I I′)
2
R (11.1)
2
2 sin (I I′) tan (I I′)
2
where I and I′ are the angles of incidence and refraction, respectively.
The first term of Eq. 11.1 gives the reflection of the light which is
polarized normal to the plane of incidence (s-polarized), and the second
term the reflection for the other plane of polarization (p-polarized). As
indicated in Sec. 10.1, at normal incidence Eq. 11.1 reduces to

(n′ n) 2
R (11.2)
(n′ n) 2

The variation of reflection from an air-glass interface as a function of
the angle of incidence (I) is shown in Fig. 11.1, where the solid line is
R, the dashed line is the sine term, and the dotted line is the tangent
term. Notice that the dotted line drops to zero reflectivity at
Brewster’s angle (Eq. 10.18).
The reflection from more than one surface can be treated as indicated
by Eq. 10.5 when the separation between the surfaces is large com-
pared to the wavelength of light. However, when the surface-to-surface
separation is small, then interference between the light reflected from

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