Solution:

Bandwidth x Length $=15 \mathrm{Mb} / \mathrm{sec} \times 4 \mathrm{~km}=(60 \mathrm{Mb} / \mathrm{sec}) \mathrm{km}$

Selecting optical source: LED at $820 \mathrm{~nm}$ is suitable for short distances. The LED generates $10 \mathrm{dBm}$ optical powers.

Selection of optical fiber: Step-index multimode fiber is selected. The fiber has bandwidth length product of $100(\mathrm{Mb} / \mathrm{s}) \mathrm{km}$.

Splicing loss $\mathrm{I}_{\mathrm{s}}=0.5 \mathrm{~dB} /$ slice

Connector loss $\mathrm{I}_{\mathrm{c}}=1.5 \mathrm{~dB}$

System link power margin $\mathrm{Pm}-8 \mathrm{~dB}$

Fiber attenuation $\alpha \mathrm{f}=6 \mathrm{~dB} / \mathrm{km}$

Actual total loss $=(2 \times \mathrm{lc})+\alpha \mathrm{fL}+\mathrm{Pm}$

$P T=(2 \times 1.5)+(6 \times 4)+8$

$\mathrm{PT}=35 \mathrm{~dB}$

Maximum allowable system loss:

$ \begin{aligned} & P_{\max }=\text { Optical source output power- optical receiver sensitivity } P_{\max }=-10 \mathrm{dBm}-(-50 \mathrm{dBm}) \\\\ & P_{\max }=40 \mathrm{dBm}\\ \end{aligned}\\ $