  We study how the sizes and radial profiles of galaxies vary with wavelength,
by fitting Sersic functions simultaneously to imaging in nine optical and
near-infrared bands. To quantify the wavelength dependence of effective radius
we use the ratio, $\mathcal{R}$, of measurements in two restframe bands. The
dependence of Sersic index on wavelength, $\mathcal{N}$, is computed
correspondingly. Vulcani et al. (2014) have demonstrated that different galaxy
populations present sharply contrasting behaviour in terms of $\mathcal{R}$ and
$\mathcal{N}$. Here we study the luminosity dependence of this result. We find
that at higher luminosities, early-type galaxies display a more substantial
decrease in effective radius with wavelength, whereas late-types present a more
pronounced increase in Sersic index. The structural contrast between types thus
increases with luminosity.
  By considering samples at different redshifts, we demonstrate that lower data
quality reduces the apparent difference between the main galaxy populations.
However, our conclusions remain robust to this effect.
  We show that accounting for different redshift and luminosity selections
partly reconciles the size variation measured by Vulcani et al. with the weaker
trends found by other recent studies. Dividing galaxies by visual morphology
confirms the behaviour inferred using morphological proxies, although the
sample size is greatly reduced.
  Finally, we demonstrate that varying dust opacity and disc inclination can
account for features of the joint distribution of $\mathcal{R}$ and
$\mathcal{N}$ for late-type galaxies. However, dust does not appear to explain
the highest values of $\mathcal{R}$ and $\mathcal{N}$. The bulge-disc nature of
galaxies must also contribute to the wavelength-dependence of their structure.
