Page 388 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 30] LIGHT 373

SOLVED PROBLEM 30.2
A marine radar operates at a wavelength of 3.2 cm. What is the frequency of the radar waves?
Radar waves are electromagnetic and hence travel with the velocity of light c. Therefore
8
c 3 × 10 m/s 9
f = = = 9.4 × 10 Hz
λ 3.2 × 10 −2 m

LUMINOUS INTENSITY AND FLUX
The eye responds to only part of the electromagnetic radiation emitted by most light sources (about 10 percent in
the case of an ordinary light bulb) and is not equally sensitive to light of different colors (the greatest sensitivity
is to yellow-green light). For these reasons the watt is not a useful unit for comparing light sources and the
illumination they provide, and other units, more closely based on the visual response of the eye, are necessary.
The brightness of a light source is called its luminous intensity I, whose unit is the candela (cd). The candela
is defined in terms of the light emitted by a blackbody (see Chapter 22) at the freezing temperature of platinum,
1773 C. The intensity of a light source is sometimes referred to as its candlepower.
◦
The amount of visible light that falls on a given surface is called luminous flux F, whose unit is the lumen
2
(lm). One lumen is equal to the luminous flux which falls on each 1 m of a sphere1min radius when a 1-cd
isotropic light source (one that radiates equally in all directions) is at the center of the sphere. Since the surface
2
2
area of a sphere of radius r is 4πr , a sphere whose radius is 1 m has 4π m of area, and the total luminous
flux emitted by a 1-cd source is therefore 4π lm. Thus the luminous flux emitted by an isotropic light source of
intensity I is given by
F = 4π I
Luminous flux = (4π) (luminous intensity)
The above formula does not apply to a light source that radiates different fluxes in different directions. In
such a situation the concept of solid angle is needed. A solid angle is the counterpart in three dimensions of an
ordinary angle in two dimensions. The solid angle (Greek capital letter omega) subtended by area A on the
surface of a sphere of radius r is given by
A
=
r 2
area on surface of sphere
Solid angle =
(radius of sphere) 2
The unit of solid angle is the steradian (sr); see Fig. 30-2. Like the degree and the radian, the steradian is a
dimensionless ratio that disappears in calculations.
The general definition of luminous flux is
F = I
Luminous flux = (luminous intensity) (solid angle)

2
2
2
Since the total area of a sphere is 4πr , the total solid angle it subtends is 4πr /r sr = 4π sr. This definition
of F thus gives F = 4π I for the total flux emitted by an isotropic source, as stated earlier. The luminous flux a
1-cd source gives off per steradian therefore equals 1 lm, and 1 cd equals 1 lm/sr.
The luminous efficiency of a light source is the amount of luminous flux it radiates per watt of input power.
The luminous efficiency of ordinary tungsten-filament lamps increases with their power, because the higher
the power of such a lamp, the greater its temperature and the more of its radiation is in the visible part of the
spectrum. The efficiencies of such lamps range from about 8 lm/W for a 10-W lamp to 22 lm/W for a 1000-W
lamp. Fluorescent lamps have efficiencies from 40 to 75 lm/W.