Opacity-induced emission-height shift
= Opacity-induced emission-height shift
{title2=$\Delta z=H\ln a$}
If optical depth is $\tau(z)=\tau_se^{-z/H}$, multiplying opacity by $a$ raises any fixed-optical-depth surface by $H\ln a$. In a constant lapse-rate layer this changes its temperature by $-\Gamma H\ln a$.