$1.$ A laser diode operates with a forward voltage of $1\mathrm{.}6$ V at a current of $45$mA$.$ Its power output into a fiber is $+8\mathrm{.}25$ dBm$.$

a$.(1)$ Calculate its efficiency.

b$.(1)$ The above source is part of a system that has a total loss of $10$ dB$.$ It is used with a detector having a sensitivity of $0\mathrm{.}8$ mA$/$mW$.$ Calculate the current at the detector.