We use the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar) linear'' potential to estimate the light quark wave function for qQ\ifmmode\bar\else\textasciimacron\fi{} mesons in the limit ${\mathrm{m}}_{\mathrm{Q}}$\ensuremath{\rightarrow}\ensuremath{\infty}. We use these wave functions to calculate the Isgur-Wise function \ensuremath{\xi}(\ensuremath{\upsilon}\ensuremath{\cdot}\ensuremath{\upsilon}\ensuremath{'}) for orbital and radial ground states in the phenomenologically interesting range 1 \ensuremath{\leqslant}\ensuremath{\upsilon}\ensuremath{\cdot}\ensuremath{\upsilon}\ensuremath{'}\ensuremath{\leqslant}4. We find a simple expression for the zero-recoil slope, \ensuremath{\xi}\ensuremath{'}(1)=-1/2-${\mathrm{\ensuremath{\epsilon}}}^{2}$〈${\mathrm{r}}_{\mathrm{q}}$${\mathrm{}}^{2}$〉/3, where \ensuremath{\epsilon} is energy eigenvalue of the light quark, which can be identified with the \ensuremath{\Lambda}\ifmmode\bar\else\textasciimacron\fi{} parameter of the heavy quark effective theory. This result implies an upper bound of -1/2 for the slope \ensuremath{\xi}\ensuremath{'}(1). Also, because for a very light quark q (q=u,d) the size 〈${\mathrm{r}}_{\mathrm{q}}$${\mathrm{}}^{2}$〉 of the meson is determined mainly by the ``confining'' term in the potential (${\ensuremath{\gamma}}_{0}$\ensuremath{\sigma}r), the shape of ${\ensuremath{\xi}}_{\mathrm{u},\mathrm{d}}$(\ensuremath{\upsilon}\ensuremath{\cdot}\ensuremath{\upsilon}\ensuremath{'}) is seen to be the most sensitive to the dimensionless ratio \ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{u},\mathrm{d}}^{2}$/\ensuremath{\sigma}. We present results for the ranges of parameters 150 MeV${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{u},\mathrm{d}}$600 MeV (\ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{s}}$\ensuremath{\approx}\ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{u},\mathrm{d}}$+100 MeV), 0.14 ${\mathrm{GeV}}^{2}$\ensuremath{\leqslant}\ensuremath{\sigma}\ensuremath{\leqslant}0.25 ${\mathrm{GeV}}^{2}$ and light quark masses ${\mathrm{m}}_{\mathrm{u}}$,${\mathrm{m}}_{\mathrm{d}}$\ensuremath{\approx}0, ${\mathrm{m}}_{\mathrm{s}}$=175 MeV and compare to existing experimental data and other theoretical estimates. Fits to the data give \ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{u},\mathrm{d}}^{2}$/\ensuremath{\sigma}=4.8\ifmmode\pm\else\textpm\fi{}1.7, -\ensuremath{\xi}${\ensuremath{'}}_{\mathrm{u},\mathrm{d}}$(1)=2.4\ifmmode\pm\else\textpm\fi{}0.7, and |${\mathrm{V}}_{\mathrm{cb}}$|${\mathrm{\ensuremath{\tau}}}_{\mathrm{B}}$/1.48 ps=0.50\ifmmode\pm\else\textpm\fi{}0.008 [ARGUS 1993]; \ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{u},\mathrm{d}}^{2}$/\ensuremath{\sigma}=3.3\ifmmode\pm\else\textpm\fi{}1.2, -${\ensuremath{\xi}}_{\mathrm{u},\mathrm{d}}^{\ensuremath{'}}$(1)=1.8\ifmmode\pm\else\textpm\fi{}0.5, and |${\mathrm{V}}_{\mathrm{cb}}$|${\mathrm{\ensuremath{\tau}}}_{\mathrm{B}}$/1.48 ps=0.043\ifmmode\pm\else\textpm\fi{}0.005 [CLEO 1993]; \ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{u},\mathrm{d}}^{2}$/\ensuremath{\sigma}=2.0\ifmmode\pm\else\textpm\fi{}0.7, -${\ensuremath{\xi}}_{\mathrm{u},\mathrm{d}}^{\ensuremath{'}}$(1)=1.3\ifmmode\pm\else\textpm\fi{}0.3, and |${\mathrm{V}}_{\mathrm{cb}}$|F(1)=0.037\ifmmode\pm\else\textpm\fi{}0.002 [CLEO 1994] [existing theoretical estimates for F(1) fall in the range 0.86(1)1.01]. Our model seems to favor the CLEO 1994 data set in two respects: the fits are better and the resulting ranges for the model parameters (\ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{u},\mathrm{d}}$, \ensuremath{\sigma}) are more in line with independent theoretical estimates.