homework and exercises - Lasers : Threshold Pump Power for Laser Oscillation

I was working my way through some basic laser problems , when I cam across this one :

Consider the ruby laser for which we have the following values of the various parameters:

$N =$ $1.6$ x $10^{19}$ $cm^{-3}$ ; $t_{sp}$ = $3$ x $10^{-3}$ $s$ ; $v_p$ = $6.25$ x $10^{14}$ $Hz$

• Find the threshold pump power for laser oscillation , $P_t$ = $Nh\nu$ $/$ $2$$t_{sp}$



• If we assume that the efficiency of the pumping source to be $25$% and also that only $25$% of the pump light is absorbed on passage through the ruby rod, then the electrical threshold power comes out to be how much ?

I am able to solve the first part but am all thumbs in the second part - can someone help me out ?

^{Disclaimer: This is not a homework question . I am preparing for a physics exam and was solving these questions / examples from the book recommended by my instructor.}

Answer

The efficiency of the pumping source is $x$ means that $x$ amount of electrical power is converted to energy which is useful for pumping the laser medium. The absorption of the pump is $y$ means that $y$ amount of the energy from the pump source is actually pumped into the medium to generate the population inversion necessary for lasing. The total amount of electrical power $P_E$ which makes it into the laser medium is therefore $x\ y\ P_E$.