Page 216 - Algae Anatomy, Biochemistry, and Biotechnology

Working with Light 199

This is interesting. From the definition of irradiance [Equation (5.9)], we know that F ¼ E A
for constant flux density across a finite surface area A. As the area A of the surface of a sphere with
radius r is given by:

2
A ¼ 4p r ¼ p D 2 (5:27)
we have:

(5:28)
F ¼ E A ¼ p I n
Given the definition of radiant exitance [Equation (5.10)] and radiance for a Lambertian surface
[Eqation (5.23)], we have:

dF
M ¼ ¼ p L (5:29)
d A
This explains, clearly and without resorting to integral calculus, where the factor of p
comes from.

UNITS CONVERSION
Radiant and Luminous Flux (Radiant and Luminous Power)
1 J (joule) ¼ 1 W sec (watt second)
1 W (watt) ¼ 683.0 lm (photopic) at 555 nm ¼ 1700.0 lm (scotopic) at 507 nm
1lm ¼ 1.464 10 23 W at 555 nm ¼ 1/(4p) candela (cd) (only if isotropic)
1 lm sec 21 (lumen seconds 21 ) ¼ 1.464 10 23 J at 555 nm.

A monochromatic point source with a wavelength of 510 nm with a radiant intensity of
1/683 W sr 21 has a luminous intensity of 0.503 cd, as the photopic luminous efficiency at
510 nm is 0.503.
A 680 nm laser pointer with the power of 5 mW produces 0.005 W 0.017 683 lm W 21 ¼
0.058 lm, while a 630 nm laser pointer with a power of 5 mW produces 0.905 lm, a significantly
greater power output.
Determining the luminous flux from a source radiating over a spectrum is more difficult. It is
necessary to determine the spectral power distribution for the particular source. Once that is done, it
is necessary to calculate the luminous flux at each wavelength, or at regular intervals for continuous
spectra. Adding up the flux at each wavelength gives a total flux produced by a source in the visible
spectrum.
Some sources are easier to do this with than others. A standard incandescent lamp produces a
continuous spectrum in the visible, and various intervals must be used to determine the luminous
flux. For sources like a mercury vapor lamp, however, it is slightly easier. Mercury emits light pri-
marily in a line spectrum. It emits radiant flux at six primary wavelengths. This makes it easier to
determine the luminous flux of this lamp versus the incandescent.
Generally, it is not necessary to determine the luminous flux for yourself. It is commonly given
for a lamp based on laboratory testing during manufacture. For instance, the luminous flux for a
100 W incandescent lamp is approximately 1700 lm. We can use this information to extrapolate
to similar lamps. Thus the average luminous efficacy for an incandescent lamp is about
17 lm W 21 . We can now use this as an approximation for similar incandescent sources at
various wattages.