$($LED Efficiencies$)$ A $1550($nm$)$ emitting LED has an active region that is doped p$-$type with a radiative lifetime of $100$ ns and a nonradiative lifetime of $50$ ns$.$ At a forward current through the LED of $50$ mA the voltage across the LED is $1\mathrm{.}1$ V and the emitted optical power is $4$ mW$.$ Calculate the following: $($a$)$ Internal quantum efficiency $($b$)$ External quantum efficiency $($c$)$ Power conversion efficiency $($d$)$ The light extraction efficiency