  Context. High latitude molecular clouds (hereafter HLMCs) permit the study of
interstellar gas dynamics and astrochemistry with good accuracy due to their
proximity, generally clear lines of sight, and lack of internal star-forming
activity which can heavily modify the physical context. MBM 40, one of the
nearest HLMCs, has been extensively studied, making it a superb target to infer
and study the dust-to-gas mixing ratio (DGMR).
  Aims. The mixing of dust and gas in the interstellar medium remains a
fundamental issue to keep track of astrochemistry evolution and molecular
abundances. Accounting for both molecular and atomic gas is difficult because
$H_2$ is not directly observable and HI spectra always show different dynamical
profiles blended together which are not directly correlated with the cloud. We
used two independent strategies to infer the molecular and atomic gas column
densities and compute the dust-to-gas mixing ratio.
  Methods. We combined $HI$ 21 cm and $^{12}CO$ line observations with the IRAS
100 $\mu$m image to infer the dust-to-gas mixing ratio within the cloud. The
cloud 21 cm profile was extracted using a hybrid Gaussian decomposition where
$^{12}CO$ was used to deduce the total molecular hydrogen column density.
Infrared images were used to calculate the dust emission.
  Results. The dust-to-gas mixing ratio is nearly uniform within the cloud as
outlined by the hairpin structure. The total hydrogen column density and 100
$\mu$m emissivity are linearly correlated over a range in $N(H_{tot})$ of one
order of magnitude.
