  We explore the luminosity L of magnetized white dwarfs and its effect on the
mass-radius relation. We self-consistently obtain the interface between the
electron degenerate gas dominated inner core and the outer ideal gas surface
layer or envelope by incorporating both the components of gas throughout the
model white dwarf. This is obtained by solving the set of magnetostatic
equilibrium, photon diffusion and mass conservation equations in the Newtonian
framework, for different sets of luminosity and magnetic field. We
appropriately use magnetic opacity, instead of Kramer's opacity, wherever
required. We show that the Chandrasekhar-limit is retained, even at high
luminosity upto about 10^{-2} solar luminosity but without magnetic field, if
the temperature is set constant inside the interface. However there is an
increased mass for large-radius white dwarfs, an effect of photon diffusion.
Nevertheless, in the presence of strong magnetic fields, with central strength
of about 10^{14} G, super-Chandrasekhar white dwarfs, with masses of about 1.9
solar mass, are obtained even when the temperature inside the interface is kept
constant. Most interestingly, small-radius magnetic white dwarfs remain
super-Chandrasekhar even if their luminosity decreases to as low as about
10^{-20} solar luminosity. However, their large-radius counterparts in the same
mass-radius relation merge with Chandrasekhar's result at low L. Hence, we
argue for the possibility of highly magnetized, low luminous
super-Chandrasekhar mass white dwarfs which, owing to their faintness, can be
practically hidden.
