Consider a layer $1$m thick located $4$m below a planar air$-$GaAs $($with refraction index n $=3\mathrm{.}6)$ detector surface. The absorption coefficient a $=105$ cm$^-1$ when the detector is operating at $850$ nm$.$

$($a$)$ Calculate the fraction of the incident power absorbed in the layer.

$($b$)$ If the detector produces $50$A of the output current for a $400$W input light bean. Calculate the resposivity and the quantum efficiency.