Page 297 - Modern Optical Engineering The Design of Optical Systems

276 Chapter Twelve

The illumination produced at point B is calculated from Eq. 12.7
(after rewriting it in photometric symbols)
2
H N sin
2
E B sin
2
1
1
2
(10L ster cm )
2
7.85 lumen cm 2
Applying the cosine-fourth law, we find the illumination at C
4
E E cos 45°
C B
7.85 (0.707) 4
1.96 lumen cm 2

Since there are 929 cm per square foot
2
E 929 1.96 1821 lumens ft 2
C
1821 footcandles

Since the surface BC has a diffuse reflectivity of 70 percent, we can
multiply the illumination in footcandles by 0.7 to obtain the brightness
in foot-lamberts

B 0.7 1821 1275 foot-lamberts

Similarly 0.7 times the illumination in lumens cm 2 will yield the
brightness in lamberts

B 0.7 1.96 1.37 lamberts

Or we can retain the lumen units, and determine that, with 1.96 lumen cm 2
falling on a surface 70 percent reflectivity, 1.37 lumen cm 2 will be
emitted into a hemisphere, and, following our previous reasoning,
compute the brightness as

1.37
B

0.44 lumen ster 1 cm 2

0.44 candle cm 2