A recent data analysis of the far-infrared (FIR) map of the Galaxy and the Magellanic Clouds has shown that there is a tight correlation between two FIR colours: the 60 um-100 um and 100 um-140 um colours. This FIR colour relation called ``main correlation can be interpreted as indicative of a sequence of various interstellar radiation fields with a common FIR optical property of grains. In this paper, we constrain the FIR optical properties of grains by comparing the calculated FIR colours with the observational main correlation. We show that neither of the ``standard grain species (i.e. astronomical silicate and graphite grains) reproduces the main correlation. However, if the emissivity index at ~ 100--200 um is changed to ~ 1--1.5 (not ~ 2 as the above two species), the main correlation can be successfully explained. Thus, we propose that the FIR emissivity index is ~ 1--1.5 for the dust in the Galaxy and the Magellanic Clouds at ~ 100--200 um. We also consider the origin of the minor correlation called ``sub-correlation, which can be used to estimate the Galactic star formation rate.
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