  Transitional discs are a special type of protoplanetary discs where planet
formation is thought to be taking place. These objects feature characteristic
inner cavities and/or gaps of a few tens of AUs in the sub-millimitre images of
the disc. This signature suggests a localised depletion of matter in the disc
that could be caused by planet formation processes. However, recent
observations have revealed differences in the structures imaged at different
wavelengths in some of these discs. In this paper, we aim to explain these
observational differences using self-consistent physical 2-D hydrodynamical and
dust evolution models of such objects, assuming their morphology is indeed
generated by the presence of a planet. We use these models to derive the
distribution of gas and dust in a theoretical planet-hosting disc, for various
planet masses and orbital separations. We then simulate observations of the
emitted and scattered light from these models with VLT/SPHERE ZIMPOL,
Subaru/HiCIAO, VLT/VISIR and ALMA. We do this by first computing the full
resolution images of the models at different wavelengths, and then simulating
the observations accounting for the characteristics of each particular
instrument. The presence of the planet generates pressure bumps in the gas
distribution of the disc whose characteristics strongly depend on the planet
mass and position. These bumps cause large grains to accumulate while small
grains are allowed into inner regions. This spatial differentiation of the
grain sizes explains the differences in the observations since different
wavelengths and observing techniques trace different parts of the dust size
distribution. Based on this effect, we conclude that the combination of
visible/near-infrared polarimetric and sub-mm images is the best strategy to
constrain the properties of the unseen planet responsible for the disc
structure.
