  Electromagnetically induced transparency (EIT) on atomic D$_{1}$ line of
rubidium is studied using a nanometric-thin cell with atomic vapor column
length in the range of L= 400 - 800 nm. It is shown that the reduction of the
cell thickness by 4 orders as compared with an ordinary cm-size cell still
allows to form an EIT resonance for $L= \lambda$ ($\lambda =794$ nm) with the
contrast of up to 40%. Remarkable distinctions of EIT formation in
nanometric-thin and ordinary cells are demonstrated. Despite the Dicke effect
of strong spectral narrowing and increase of the absorption for $L=$ $\lambda
/2$, EIT resonance is observed both in the absorption and the fluorescence
spectra for relatively low intensity of the coupling laser. Well resolved
splitting of the EIT resonance in moderate magnetic field for $L=$ $\lambda $
can be used for magnetometry with nanometric spatial resolution. The presented
theoretical model well describes the observed results.
