Page 260 - Modern Optical Engineering The Design of Optical Systems

240 Chapter Eleven

The reflectivity of a surface coated with one thin film is given by the
equation
r r 2r r cos X
2
2
1
2
1 2
R (11.3)
2
1 r r 2r r cos X
2
1 2 1 2
where
4 n t cos I
1 1
1
X (11.4)

sin (I 0 I 1) tan (I 0 I 1)
r or (11.5)
1
sin (I I ) tan (I I )
0 1 0 1
sin (I 1 I 2) tan (I 1 I 2)
r or (11.6)
2
sin (I I ) tan (I I )
1 2 1 2
and is the wavelength of light; t is the thickness of the film; n 0 , n 1 ,
and n 2 are the refractive indices of the media; and I 0 , I 1 , and I 2 are
the angles of incidence and refraction. Figure 11.2 shows a sketch of
the film and indicates the physical meanings of the symbols. The sine
or tangent expressions for r 1 and r 2 are chosen depending on the polari-
zation of the incident light as in Eq. 11.1; for unpolarized light, which
is composed equally of both polarizations, R is computed for each polari-
zation and the two values are averaged. If we assume nonabsorbing
materials, the transmission T equals (1 R). At normal incidence I 0
I 1 I 2 0, and r 1 and r 2 reduce to
n n
0
r 1 (11.7)
1 n n
0 1
n 1 n 2
r (11.8)
2 n n
1 2

Figure 11.2 Passage of light ray
through a thin film, indicating
the terms used in Eq. 11.3.