A disc shaped photoelectric detector of area 0.5 cm 2 generates current when light of frequency that of yellow light falls on it. The photoelectron generation efficiency is 20%. In the arrangement s

Question

A disc shaped photoelectric detector of area $0.5 cm^{2}$ generates current when light of frequency > that of yellow light falls on it. The photoelectron generation efficiency is 20%. In the arrangement shown, S is an isotropic 100 watt point monochromatic light source with $λ = 4000 \overset{˚}{A}$ . The focal of the lens is 20 cm and its circular area is $4 cm^{2}$ . Find the photocurrent (in mA) in the detector assuming all rays to be paraxial w.r.t. lens.

Point source S, lens at 30 cm, photo detector at 90 cm from the lens

TestHub · Accepted Answer

Image by lens: v 1 ​ = 20 1 ​ − 30 1 ​ v = 60 cm Power on lens: 100 × 4 π × 3 0 2 4 ​ = 0.0354 W Lens radius = 1.128 cm Beam radius at 90 cm = 1.128 × 60 30 ​ = 0.564 cm Beam area = 1 c m 2 Detector (0.5 cm²) gets half: 0.0177 W Photon energy = 3.1 eV I = 0.2 × 3.1 × 1.6 × 1 0 − 19 0.0177 ​ × 1.6 × 1 0 − 19 = 1.14 mA

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