OPTICS OF THE RAINBOW AND THE PHYSICS OF RAIN 285 
|\Omm 
imp 20 
0.63 
OTe eae 
mie =| (0) | a 3 4 
Fic. 9—Theoretical monochromatic rainbow intensities, (a) for the Airy theory, single drop size; 
(b) line I for a rain with a Gaussian size distribution; (c) line II for shower rain, III for warm front 
rain, and IV for drizzle (see Fig. 8 b). For the mean rainbow: z = 0.63 (2r7ro/d)?3(@ — go), yo = 0.5 mm 
for model II to IV, and ¢) = geometric rainbow angle 
Because the intensity of the rainbow increases 
with drop size (geometric scattering intensity 
~r, Airy intensity ~7"/°-\7'/°) the efficiency of 
drops for rainbow intensity is very broad and 
has a weak maximum near 1.0 to 0.6 mm (Fig. 
8 a’ and b’). 
The rainbow intensities in Figure 9 were cal- 
culated corresponding to various raindrop dis- 
tributions. These rainbows have almost entirely 
lost the secondary Airy bows. The divergence of 
the sunlight would destroy the secondary bows 
even more. 
Calculations of the absolute intensity of rain- 
bow are shown in condensed form in Table 1. If 
we neglect the extinction of light by the rain it- 
self the intensity of the rainbow should increase 
with the rain intensity. However the extinction 
of a sereen of falling raindrops also increases 
TasBLe 1—Erxtinction of rain and brightness 
of the rainbow 
| 
Rainfall rate (mm/h) }) al 5 25 
Drop numbers (em~? Km) 34.5 |50.0 |205.0 
Extinction coefficient (Km!) 0.19) 0.45) 1.338 
Visibility range (Km) ZION 820 ||) .30 
Brightness of rainbow* 
(unit: 1076 Sun disk 
brightness) | 
without extinction 6.4 | 9.4 | (38) 
with extinction Sel aeono! (Od) 
* Rain falling from 1 km height, Sun altitude 
and angle of view to the horizontal 21°; no rain 
between Sun and observer. 
with rainfall intensity and, as a result, rainbow 
brightness for normal conditions is nearly inde- 
pendent of the rain intensity. In green light the 
principal rainbow maximum is roughly three 
times as bright as the clear-sky brightness. 
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