Page 255 - Modern Optical Engineering The Design of Optical Systems

Optical Materials 235

ANSWER: (a) Each additional cm of material reduces the transmission by a
factor of 0.80/0.85 = 0.941176.
Thus for 3 cm we get T 0.8 0.941176 0.752941
(b) Neglecting all multiple reflections T T T and by
SURFACE ABSORBTION
Eq. 10.3, T e ax , so:
A
T T e at t 1.0 0.85 T e a
s s
t 2.0 0.80 T e 2a
s
T 0.85e a 0.80e 2a
s
e a 0.80/0.85 0.941176
a log 0.941176 0.06062462 cm 1
e
3 Determine the coefficients for the dispersion equation, Eq. 10.8 given in
Sec. 10.1 for BK7 glass as given in Fig. 10.4, using the d(.5876), C(.6563), and
F(.4861) lines. Calculate the index for the r (.7065), g (.4358), and h (.4047)
lines and compare with the entries in Fig. 10.4.
ANSWER: To get the coefficients, solve three simultaneous equation versions of
Eq. 10.8 using the wavelengths given above and the indices from Fig. 10.4. Put
the coefficients into Eq. 10.8 and determine the indices using the wavelengths
for r, g, and h as given above.
4 Plot the spectral transmission curve which will result if the filters c and f
shown in Fig. 10.10 are combined.
ANSWER: From the figure, determine the transmission of each filter for several
wavelengths between 450 nm and 600 nm. Multiply the transmissions at each
wave length to get the transmission of the combination at that wavelength.