Effects of Pollution on Visibility, Ultraviolet Radiation, and Colors in the Sky - Air Pollution and Global Warming: History, Science, and Solutions - page 162

where n is the real index of refraction (dimensionless),

Incident Reflected

is the angle of incidence or refraction, and subscripts
1 and 2 refer to media 1 and 2, respectively. The real
index of refraction is the ratio of the speed of light
in a vacuum ( c

1 3

Air

10 8 ms − 1 )tothat in a = 2.99792 ×

Water

different medium ( c 1 ,ms − 1 ). Thus,

2

c
c 1

n 1 = (7.6)

Refracted

Because light cannot travel faster than its speed in a
vacuum, the real index of refraction of a medium other
than a vacuum must exceed unity. The refractive index
of air at a wavelength of 0.5

Figure 7.13. Examples of reflection and refraction.
During reflection, the angle of incidence ( 1 )equals

the angle of reflection ( 3 ). During refraction, the

angles of incidence and refraction are related by
Snell's law. The line perpendicular to the air-water
interface is the surface normal.

mis1.000279. Real
refractive indices of some liquids and solids are given
in Table 7.2.

7.1.4. Aerosol and Hydrometeor
Particle Scattering
Particle scattering is the redirection of incident energy
by a particle without a loss of energy to the particle.
Particle scattering is really the combination of several
processes, including reflection, refraction, and diffrac-
tion. These processes are discussed next.

Example 7.3
(a) Suppose light at a wavelength of 0.5 m

travels between the atmosphere (medium 1)
and liquid water (medium 2) and the angle
between the incident light and the surface
normal 45 ◦ .Byhowmany degrees

is the light bent toward the surface normal
when it enters medium 2?
(b) Do the same calculation for light traveling
between outer space (medium 1) and the
atmosphere (medium 2).

is 1 =

7.1.4.1. Reflection
Reflection occurs when radiation bounces off an object
at an angle equal to the angle of incidence. No energy
is lost during reflection. Figure 7.13 shows an example
of reflection. Radiation can reflect off aerosol particles,
cloud drops, and other surfaces. The colors of most
objects that we see are due to preferential reflection
of certain wavelengths by the object. For example, an
apple appears red because the apple's skin absorbs blue
and green wavelengths and reflects red wavelengths to
our eye.

Solution
(a) At a wavelength of 0.5 m, the real index

of refraction of air is n 1 = 1.000279 and

that of liquid water is n 2 1.335. From

Equation 7.5, the angle between the light
and the surface normal

=

in medium 2 is

32 ◦ ;thus,the light is bent by 13 degrees
toward the surface normal when it enters
water from the atmosphere.
(b) At a wavelength of 0.5

2 =

m, the real index
of refraction of a vacuum is n 1 1.0. From

Equation 7.5, the angle between the light
and the surface normal

=

7.1.4.2. Refraction
Refraction occurs when a wave or photon leaves a
medium of one density and enters a medium of another
density. In such a case, the speed of the wave changes,
changing the angle of the incident wave relative to a
surface normal, as shown in Figure 7.13. If a wave
travels from a medium of one density to a medium of
ahigher density, it bends (refracts) toward the surface
normal (the vertical line in Figure 7.13). The angle of
refraction is related to the angle of incidence by Snell's
law :

in medium 2 is 2

44.984 ◦ ;thus,the light is bent by 0.016
degrees toward the surface normal when it
enters the atmosphere from space.

=

In sum, the angle of refraction between the
atmosphere and water is much greater than that
between space and the atmosphere.

Because the real index of refraction is wavelength
dependent, different wavelengths are refracted by dif-
ferent angles when they pass from one medium to
another. For instance, when visible light passes from

n 2
n 1 =

sin 1

(7.5)

sin 2