A firefly's glowing abdomen is modelled as a small Lambertian source of radiance W m…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Photodetection, photonic sources and quantum optics · Photodetection, photonic sources and quantum optics

Optics and Photonics, Ch The photon

Problem

A firefly's glowing abdomen is modelled as a small Lambertian source of radiance L=10L = 10 W m−2^{-2} sr−1^{-1} at λ=560\lambda = 560 nm, with emitting area As=4.0A_s = 4.0 mm2^2. A photon-counting detector of collecting area Ar=4.0A_r = 4.0 cm2^2 faces the firefly directly at a distance r=2.0r = 2.0 m, so it subtends a solid angle Ω=Ar/r2\Omega = A_r/r^2 at the source (the small-angle Lambertian result of Chapter 3). Assume no loss between source and detector. ((a)) Using Φ=LAsΩ\Phi = LA_s\Omega, find the radiant flux collected and hence the photon flux (photons per second) reaching the detector. ((b)) Assuming every photon that arrives is absorbed, find the force this light exerts on the detector. ((c)) The light is then attenuated by a neutral-density filter of transmittance 10−810^{-8} and sent into a two-beam interferometer whose mirror is scanned through 100 fringes of visibility V=0.90\mathcal V = 0.90. Taking well above the counting noise to mean at least 100/V2100/\mathcal V^2 photons entering the interferometer during each fringe, estimate the minimum total observing time for the fringe pattern to emerge.

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