  The paper deals with the Raychaudhuri equation (RE) which is a non-linear
ordinary differential equation in $\Theta$, the expansion scalar corresponding
to a geodesic flow. Focusing theorem which follows as a consequence of the RE
has been restated in terms of the cosmic parameter $q$ (deceleration parameter)
both for Einstein gravity and for modified gravity theories. Measurable
quantities namely the luminosity distance and density parameter are shown to
have an upper bound using the Raychaudhuri scalar. An analogy between geometric
and cosmological RE has been made. Subsequently, to find the solution of the
non-linear RE a transformation of variable related to the metric scalar of the
hyper-surface has been identified which converts the former to a second order
differential equation. Finally, the first integral of this second order
differential equation gives the entire picture of the dynamics of cosmic
evolution.
