This note originally posted to VSNET. -- MWR
Berto Monard asked about transformations from (V-R) to visual magnitudes. I did some calculations awhile back for Janet Mattei using the CIE response curves for photopic (bright adapted eye) and scotopic (dark adapted eye) eyes, along with Johnson/Cousins curves and the Gunn-Stryker spectrophotometric atlas. The results were:
P = V -0.001 -0.066(B-V) = V -0.010 -0.073(V-R) S = V -0.006 +0.382(B-V) = V +0.031 +0.448(V-R)
These relations are reasonably good for colors < 1.5.
Whose eyes are scotopic and whose are photopic? Beats me, and I certainly don't want to get into any arguments -- I'm not any kind of expert here. The normally quoted transformation is v = V +0.2(B-V), which falls inbetween these relations. The main point is that (B-V) and (V-R) both give similar transformations, and so both should be ok for determining visual magnitudes from photometric magnitudes/colors. The (V-R) fit is somewhat worse since you are extrapolating to the bluer visual magnitudes (especially the bluer dark adapted eye) rather than bracketing them, but R is certainly easier to measure with most amateur CCDs than is B.