  The wavelength dependence of the Kormendy relation (KR) is well characterised
at low redshift but poorly studied at intermediate redshifts. The KR provides
information on the evolution of the population of early-type galaxies (ETGs).
Therefore, by studying it, we may shed light on the assembly processes of these
objects and their size evolution. As studies at different redshifts are
generally conducted in different rest-frame wavebands, it is important to
investigate whether the KR is dependent on wavelength. Knowledge of such a
dependence is fundamental to correctly interpreting the conclusions we might
draw from these studies. We analyse the KRs of the three Hubble Frontier Fields
clusters, Abell S1063 (z = 0.348), MACSJ0416.1-2403 (z = 0.396), and MACS
J1149.5+2223 (z = 0.542), as a function of wavelength. This is the first time
the KR of ETGs has been explored consistently over such a large range of
wavelengths at intermediate redshifts. We exploit very deep HST photometry,
ranging from the observed B-band to the H-band, and MUSE integral field
spectroscopy. We improve the structural parameter estimation we performed in a
previous work by means of a newly developed Python package called morphofit.
With its use on cluster ETGs, we find that the KR slopes increase smoothly with
wavelength from the optical to the near-infrared (NIR) bands in all three
clusters, with the intercepts becoming fainter at lower redshifts due to the
passive ageing of the ETG stellar populations. The slope trend is consistent
with previous findings at lower redshifts. The slope increase with wavelength
implies that smaller ETGs are more centrally concentrated than larger ETGs in
the NIR with respect to the optical regime. As different bands probe different
stellar populations in galaxies, the slope increase also implies that smaller
ETGs have stronger internal gradients with respect to larger ETGs.
