Sorry for the fundamental and basic question, Does the power of the beam that is falling on lens is equal to the power of the beam after passing through lens. Suppose If I used convex lens to converge a divergent beam of power P then the power of the beam at focus is also equal to p? My understanding is only intensity changes but when I tried calculating this power for a gaussian beam my math seem to be off. Lets take power density of sun and strip away the spectral properties for ease in calculations then power falling on the lens would be
$P=0.14w/cm^2(power density)*Pi*s^2$ s-size of lens
power after focusing would be
$P=0.14*pi*W^2$ w-beam waist
These two would be different. So, where am I going wrong.