From this result, we can compute the luminous intensity of the Sun. Since the Sun emits light equally in
all directions (is isotropic), the luminous intensityIof the Sun is
ID
ˆ
(50.7)
D
3:75 1028 lm
4sr(50.8)
D2:98 1027 candelas: (50.9)In summary, for the Sun, we find- Luminous flux:ˆsD3:75 1028 lm
- Luminous intensity:IsD2:98 1027 cd
- Illuminance at Earth:EsD 133 klx
50.5 Example: Incandescent Light Bulb
A 60-watt incandescent light bulb emits a luminous flux of 820 lumens. If this light bulb is isotropic and is
the only illumination in a room, then what is the illuminance at a distance of 80 cm from the light bulb?
Solution.From Eq. (50.2), the illuminanceEis
ED
ˆ
A
(50.10)
D
ˆ
4r^2(50.11)
D
820 lm
4.0:80m/^2(50.12)
D 102 lx (50.13)50.6 Astronomical Photometry
In astronomy, the brightness of celestial bodies such as stars and planets is not measured in the photomet-
ric units just described; instead, a logarithmic scale ofmagnitudesis employed. The magnitude scale was
originally defined so that the brightest stars in the sky are magnitude 0, the dimmest visible to the unaided
human eye are magnitude 5, and a magnitude 0 star is 100 times as bright as a magnitude 5 star. (Note that
magnitudes measuredimness, not brightness. The larger the magnitude, the dimmer the star.) The magnitude
scale is logarithmic, so an increase of 1 magnitude corresponds to a decrease in the brightness of the star by
a factor of^5
p
100 2:5119.
There are two types of magnitudes defined: theapparent magnitudeis the brightness of a star as seen
from Earth; a star’s apparent magnitude depends both on its intrinsic brightness and on its distance from
Earth. Theabsolute magnitudeis a measure of intrinsic brightness alone: is the brightness a star would have
if it were at a standard distance of 10 parsecs, or3:0857 1017 meters. It is straightforward to show that the
apparent magnitudemis related to the absolute magnitudeMby
MDm5.log 10 D1/; (50.14)whereDis the distance to the star in parsecs. (Notice that ifD D 10 parsecs, then this formula gives
MDm, as expected.)