  We present a detailed optical spectroscopic and B,V,I,Halpha photometric
study of the metal-deficient cometary blue compact dwarf (BCD) galaxy SBS
1415+437. We derive an oxygen abundance 12+log(O/H)=7.61+/-0.01 and 7.62+/-0.03
(Z =Zsun/20) in the two brightest H II regions, among the lowest in BCDs. The
helium mass fractions in these regions are Y=0.246+/-0.003 and 0.243+/-0.010.
Four techniques based on the equivalent widths of the hydrogen emission and
absorption lines, the spectral energy distribution and the colours of the
galaxy are used to put constraints on the age of the stellar population in the
low-surface-brightness (LSB) component of the galaxy, assuming two limiting
cases of star formation (SF), the case of an instantaneous burst and that of a
continuous SF with a constant or a variable star formation rate (SFR). The
spectroscopic and photometric data for different regions of the LSB component
are well reproduced by a young stellar population with an age t<250 Myr,
assuming a small extinction in the range A(V)= 0-0.6 mag. Assuming no
extinction, we find that the upper limit for the mass of the old stellar
population, formed between 2.5 Gyr and 10 Gyr, is not greater than ~(1/20 - 1)
of that of the stellar population formed during the last ~250 Myr. Depending on
the region considered, this also implies that the SFR in the most recent SF
period must be 20 to 1000 times greater than the SFR at ages > 2.5 Gyr. We
compare the photometric and spectroscopic properties of SBS 1415+437 with those
of a sample of 26 low-metallicity dwarf irregular and BCD galaxies. We show
that there is a clear trend for the stellar LSB component of lower-metallicity
galaxies to be bluer. This trend cannot be explained only by metallicity
effects. There must be also a change in the age of the stellar populations.
