OPTICS OF THE RAINBOW AND THE PHYSICS OF RAIN 
second raises the question of the oscillations of 
falling raimdrops. Other developments in rain- 
bow theory concern the effect of actual drop size 
distributions and the comparison of calculated 
and observed rainbow brightness. Further details 
may be seen in a review article [Volz, 1960}. 
The unusually fine photograph by Clarke 
[1920] (Fig. 1) illustrates well some of the im- 
portant results of the Airy theory [see Pernter 
and Haner, 1922; van de Hulst, 1957]. The pri- 
mary rainbow, and some secondary bows caused 
by interference, can be seen. The distance of a 
rainbow in monochromatic light from the anti- 
solar point depends upon the refractive index of 
water and therefore slightly upon the wave- 
length; consequently, the rainbow shows colors 
in natural light. The overall width of the in- 
tensity distribution depends upon the radius of 
the raindrops (proportional to (\/1°/°). Small 
drops give a broad rainbow with well separated 
—> 1 (mm) 
4 
2 SEAS r6m 8) On LS 3.4 516 uD 
b/o 1-0 — x OmolS 
= 
09 ioe OE 
MEASUREMENTS : qo 
og L BLANCHARD b/o > 20s iS 
5 MAGONO b/o // EQ\ yo 30° O & 
f= 07 MAGONO single drops -e =0° 
5 \ O¢(H=0°) 
« UPPET half of drop —\ 
on 06 lower eT pCeCr ORG \l a 
x 0.5; THEORY : 
IMAL I 
O4F sPILHAUS SP 
| 
Fic. 2—Deformation of falling raindrops; ratio 
of the vertical to the horizontal axis from both 
measurements and calculations 
Fic. 3—Path of 
through a falling raindrop of 2.4 mm radius, scat- 
tered in the vertical plane 
horizontal incident light 
281 
210° 
180° 
° 
150 ts b 
x 20 
5 > A: 
120 a 
Ho Ss 
fo) 
90° 7) 
5 
2 ead 
60 wy 
oe 
= 
30° 5 
z2 
a 
joa 
10D Go. 
DISTANCE OF RAINBOW 
FROM ANTI-SOLAR POINT 
LARGER=— -—*SMALLER 
+10° O 
Fic. 4—Variation of the rainbow angle ¢o with 
the angle x between the incoming light and the 
major axis respectively, the solar height H; for 
a drop with the cross section of (a) an ellipse, by 
Moebius [1907]; (b) a flattened raindrop (vertical 
plane), measured by the author on a similar shaped 
water stream 
supernumeraries. The close supernumeraries of 
larger drops are washed out by the divergence 
of the Sun’s rays. Only rain consisting of small 
and very uniform drops can give a rainbow such 
as that shown in Figure 1. 
The supernumerary bow—The disappearance 
of supernumerary bows towards the foot of the 
rainbow is a long-established result [Poey, 1863] 
clearly to be seen in some modern color photo- 
graphs. It might be supposed that this phe- 
nomenon is caused by increasing drop size be- 
cause of collisions and evaporation during fall. 
However, it seems that this cannot be the prin- 
cipal reason because the spacing between the 
mean bow and the supernumeraries is constant. 
Furthermore the calculations of Rigby and Mar- 
shall [1952] show no significant change of drop 
size distribution by collision with low rainfall 
intensities. Another possibility which must be in- 
vestigated is the shape of the falling drops. 
Drop shape and the rainbow—The Airy the- 
ory assumes that the raindrops are spheres, and 
yet we know from the experiments [Lenard, 
