$12\mathrm{.}29.$ A "laser diode" converts current to light $($as in laser pointers$).$ We wish to design a circuit that delivers a well$-$defined current to a laser diode. Shown in Fig. $12\mathrm{.}97$ is an example in which resistor $R_M$ measures the current flowing through $D_1$ and amplifier $A_1$ subtracts the resulting voltage drop from $V_{in}.$ Assume $R_M$ is very small and $V_A=.$

$($a$)$ Following the procedure used in Example $12\mathrm{.}21,$ determine the openloop gain.

$($b$)$ Calculate the loop gain and the closedloop gain.