Some examples: the brightest star in the sky, Sirius (in the constellation Canis Major), has an apparent
magnitude of1:44. Polaris (the North Star) is a variable star that varies in magnitude, but has an average
magnitude ofC1:97. The Sun has an apparent magnitude of26:72, and an absolute magnitude ofC4:85.
One the brightest stars in the sky is the blue-white supergiant Deneb (in the constellation Cygnus). Most
of the bright stars in the sky are around 50–100 light-years from Earth, but Deneb is some 1500 light-years
away, so it must be intrinsically very bright. Indeed, Deneb has an apparent magnitude ofC1:25and an
absolute magnitude of7:13.
It is possible to convert between the magnitude scale and conventional photometric units by using the Sun
as a calibration point. To convert between apparent magnitudemand illuminance, the formula can be shown
to be
EDEs 10 2
5 .mms/; (50.15)whereEis the illuminance due to the star (in lux),Esis the illuminance due to the Sun at the Earth (EsD
133;000lux),mis the apparent magnitude of the star, andmsis the apparent magnitude of the Sun (msD
26:72). Similarly, to convert between absolute magnitudeMand luminous fluxˆand luminous intensity
IDˆ=.4sr/, the formulæ are found to be (using Eqs. (50.14) and (50.15))
ˆDˆs 10 (^25) .MMs/
(50.16)
IDIs 10
(^25) .MMs/
(50.17)
whereˆsD3:75 1028 lm is the luminous flux of the Sun,IsD2:98 1027 cd is the luminous intensity
of the Sun,Mis the absolute magnitude of the star, andMsDC4:85is the absolute magnitude of the Sun.
Example.The illuminance at Earth due to light from star Sirius (apparent magnitudemD1:44)is
EDEs 10
(^25) .mms/
D.133;000lux/10
(^25) Œ1:44.26:72/
D10:28 lx
Example.The luminous fluxˆof the star Deneb (absolute magnitudeMD7:13)is
ˆDˆs 10
(^25) .MMs/
D.3:75 1028 lm/10
2
5 .7:134:85/
D2:32 1033 lm
which means Deneb is intrinsicallyˆ=ˆsD62;000brighter than the Sun. We can similarly find the luminous
intensityIof Deneb:
IDIs 10
(^25) .MMs/
D.2:98 1027 cd/10
2
5 .7:134:85/
D1:85 1032 cd
or 185nonillioncandelas.