Page 272 - Modern Optical Engineering The Design of Optical Systems

252 Chapter Eleven

Rancourt, J., Optical Thin Films, New York, McGraw-Hill, 1987.
Scharf, P., in Kingslake (ed.), Applied Optics and Optical Engineering, Vol. 1, New York,
Academic, 1965 (filters).
Thelen, A., Design of Optical Interference Coatings, New York, McGraw-Hill, 1988.
Vasicek, A., Optics of Thin Films, Amsterdam, North Holland, 1960.

Exercises

1 Plot, in the manner of Fig. 11.1, the curve of reflection against angle of inci-
dence for a single surface of glass (n 1.52), coated with a quarter wavelength
of magnesium fluoride (n 1.38).
ANSWER: Use Eq. 11.3 to 11.6 with the following:
n 1.0
0
n 1.38
1
n 1.58
2
Eq. 11.4 X (4 n t cos I )/ [4 (
4) cos I ]/ cos I
1 1 1 1 1
sin I (n /n ) sin I (1.0/1.38) sin I
1 0 1 0 0
sin I (n /n ) sin I (1.0/1.52) sin I
2 0 2 0 0
Using Eq. 11.5 to determine the two values for r and Eq. 11.6 for the two values
1
of r and Eq. 11.3 to determine the reflectance for both planes of polarization,
2
we get:
angle I R( ) R( ) R average
0
0 1.26% 1.26% 1.26%
20 1.56% 1.01% 1.28%
40 3.11% 0.32% 1.71%
50 5.31% 0.03% 2.67%
51 5.64% 0.02% 2.83%
52 5.99% 0.03% 3.01%
53 6.37% 0.04% 3.21%
55 7.23% 0.11% 3.67%
60 10.08% 0.60% 5.34%
80 44.94% 24.32% 34.63%
90 100.0% 100.0% 100.0%