Absolute magnitudes with dust extinction I have a distant $z\sim3$ galaxy with absolute AB magnitudes $M_B$ and $M_I$, where the central wavelengths of the $B$ and $I$ passbands are $\sim0.4\,\mu\text{m}$ and $\sim0.8\,\mu\text{m}$, respectively.

If this galaxy was to experience $1\,\text{mag}$ of $V$-band extinction due to dust within it, where the central wavelength of the $V$ passband is $\sim0.5\,\mu\text{m}$, how do I work out what the absolute magnitudes $M_B$ and $M_I$ would be?

Thanks for any help with this issue.
Check this lecture note. I believe there is everything you need to understand how to proceed. In brief, you should have extra information about the relative absorption, shown in the table on p.18. Given the correction in one band (which you already have $A_V = 1)$, you can find the correction in other bands using the table.

Note that the relative absorption is different for different scenario, e.g., different RADEC, different host, different type of stars.

Also note that there are two types of extinction: galactic and extragalactic.