Solution:
Source power Ps
$=0.1 \mathrm{~mW}$
$
P_s=-10 \mathrm{dBm}\\
$
Since $\quad N A=0.25$
Coupling loss
$=-10 \log \left(N A^2\right)$
$
=-10 \log \left(0.25^2\right)\\
$
$
=12 \mathrm{~dB}\\
$
Fiber loss $=\alpha_f \times L$
$
I_f=(6 \mathrm{~dB} / \mathrm{km})(0.5 \mathrm{~km}) \mathrm{I}_{\mathrm{f}}=3 \mathrm{~dB}\\
$
Connector loss $=2(2 \mathrm{~dB})$
$
I_c=4 \mathrm{~dB} \text { Design margin } P_m=4 \mathrm{~dB}\\
$
Actual output power Pout = Source power $-(\Sigma$ Losses $) P_{\text {out }}=10 \mathrm{dBm}-[12 \mathrm{~dB}+3+4+4]$
$
P_{\text {out }}=-33 \mathrm{dBm}\\
$
Since receiver sensitivity given is $-35 \mathrm{dBm}$.
$
P_{\min }=-35 \mathrm{dBm}\\
$
As $P_{out} \gt P_{\min }$, the system will perform adequately over the system operating life.