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Interstellar and atmospheric heterochromatic extinction can be treated by similar transformation methods.
Using standard passbands, an accepted average optical interstellar extinction law, and Kurucz flux tables, we derive useful colour-dependent interstellar extinction relations for UBVRI and CMT$_1$T$_2$ broad band photometric systems. For bands blueward of 500nm the reddenings for main sequence stars and evolved stars are quite different, and even can be highly non--linear and non--monotonic as a function of colour.
We have also explored the functional dependence of the interstellar extinction curves on abundance and find that the differences are not as important in the Johnson--Cousins as in the Washington system. We compute new theoretical reddening vectors in both systems.
In two broadband systems, Johnson-Cousins UBVRI and Washington CMT$_1$T$_2$, we find the dependence of atmospheric extinction on colour and on macro features in the spectra of stars, such as the Balmer jump, as parameterized by $T_{\rm eff}$, log$\,g$, and [Fe/H] in the library of Kurucz flux tables. The true broadband atmospheric extinction is far more complicated than any current reduction (transformation) methods consider. Thus all broadband magnitude systems are fundamentally unphysical -- they are not the extra--atmospheric magnitudes, but magnitudes whose relation to physical magnitudes is unknown, but may differ by 0.05 mag in some cases. Hence, it it hazardous to compare them to any synthetic magnitude system derived from either synthetic spectra or spectral scans.
