  We present spectroscopic tests of MIR to FIR extinction laws in IRDC
G028.36+00.07, a potential site of massive star and star cluster formation. Lim
& Tan (2014) developed methods of FIR extinction mapping of this source using
${\it Spitzer}$-MIPS ${\rm 24\mu m}$ and ${\it Herschel}$-PACS ${\rm 70\mu m}$
images, and by comparing to MIR ${\it Spitzer}$-IRAC $3$--${\rm 8\mu m}$
extinction maps, found tentative evidence for grain growth in the highest mass
surface density regions. Here we present results of spectroscopic infrared
extinction (SIREX) mapping using ${\it Spitzer}$-IRS (14 to ${\rm 38\mu m}$)
data of the same IRDC. These methods allow us to first measure the SED of the
diffuse Galactic ISM that is in the foreground of the IRDC. We then carry out
our primary investigation of measuring the MIR to FIR opacity law and searching
for potential variations as a function of mass surface density within the IRDC.
We find relatively flat, featureless MIR-FIR opacity laws that lack the
$\sim{\rm 12\mu m}$ and $\sim{\rm 35\mu m}$ features associated with the thick
water ice mantle models of Ossenkopf & Henning (1994). Their thin ice mantle
models and the coagulating aggregate dust models of Ormel et al. (2011) are a
generally better match to the observed opacity laws. We also find evidence for
generally flatter MIR to FIR extinction laws as mass surface density increases,
strengthening the evidence for grain and ice mantle growth in higher density
regions.
