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Apparent and Absolute Magnitudes
Apparent MagnitudeApparent magnitude m of a star is a number that tells how bright that star appears at its great distance from Earth. The scale is "backwards" and logarithmic. Larger magnitudes correspond to fainter stars. Note that brightness is another way to say the flux of light, in Watts per square meter, coming towards us. On this magnitude scale, a brightness ratio of 100 is set to correspond exactly to a magnitude difference of 5. As magnitude is a logarithmic scale, one can always transform a brightness ratio B2/B1 into the equivalent magnitude difference m2-m1 by the formula: m2-m1 = -2.50 log(B2/B1). You can check that for brightness ratio B2/B1=100, we have log(B2/B1) =log(100)= log(102) = 2, and then m2-m1=-5, the basic definition of this scale (brighter is more negative m). One then has the following magnitudes and their corresponding relative brightnesses: magnitude m | 0 1 2 3 4 5 6 7 8 9 10 ---------------------------------------------------------------- relative | 1 2.5 6.3 16 40 100 250 630 1600 4000 10,000 brightness | ratios | (Note that the lower row of numbers is just (2.512)m.)
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