Misconceptions about astronomical magnitudes

The present system of astronomical magnitudes was created as an inverse scale by Claudius Ptolemy in about 140 A.D. and was defined to be logarithmic in 1856 by Norman Pogson, who believed that human eyes respond logarithmically to the intensity of light. Although scientists have known for some time that the response is instead a power law, astronomers continue to use the Pogson magnitude scale. The peculiarities of this system make it easy for students to develop numerous misconceptions about how and why to use magnitudes. We present a useful exercise in the use of magnitudes to derive a cosmologically interesting quantity (the mass-to-light ratio for spiral galaxies), with potential pitfalls pointed out and explained. (C) 1997 American Association of Physics Teachers.