er:
1
er “peor
coverage
&
late
pew
rw ieee BL
~
teal ee
|
Cc
n = concentration of particles in air
E = original intensity of radiation
Ey = intensity after radiation has passed through y cm. of
the dusty layer
= wave length of radiation
y = distance trave-ied by radiation in the dusty layer and
in a path normai to it
Humphreys assumed that the dielectric constant of the volcanic
ash particles was 7,
This means that the index of refraction
of the particles would be which is considered to be quite
high. In this study it has been assumed that the dust particles
have an index of refraction of 1.55,
For index of refraction
equal tov, the value of h is as follows:
h = 11717
= ------ eee ee Equation 3
For an index of 1.55, h' has the value of
ht
= 2.177?
ye
4
heewe ee = © -Eguation 4
Humphreys, using the value for h given by Equation 3,
calculated that for dust particles of 1.85 micron diameter
the eoler radiation is shut out 30 times more efficiently
than terrestrial radiation, but if the value for h' is
substituted it is seen that solar radiation is shut out
approximately 160 times more efficiently.
Ze
Equation for Diffuse Reflection
According to Rayleigh, if the particles are large compared
to the wave length of solar radiation, the following equation
applies:
Ty *le
“277 r* ox
ss+e#-fe eee = 2 + “Equation 5
Humphreys used Equation 5 to determine that the total amount
of 1.85 micron volcanic dust required aloft is 1.734 x 1024
to reduce solar radiation by 10% when the sun is at the zenith,
In checking Humphreys calculetions it seems obvious that he
must have made a mistake, because if the necessary values
are substituted in Equation 5 it turns out that 1.1 x 1025
particles are required eloft,.
Be
Mie's Theory of Scatter
-
The complete rigorous theory for the scattering of light by
isotropic spherical particles was developed by Mie.
The Mie
cee ee
5004630
C2=38529