A large matt wall is uniformly lit and behaves as a Lambertian surface of radiance W m sr
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging
Optics and Photonics, Ch Radiometry and photometry
Problem
A large matt wall is uniformly lit and behaves as a Lambertian surface of radiance L=20 W m−2 sr−1. You look at it straight on, first from r1=2.00 m and then from r2=6.00 m. Model the eye as a lossless imaging system with a circular pupil of diameter 5.0 mm whose retina lies 22 mm behind the pupil. Because the wall is far compared with 22 mm, a patch of wall at distance r forms a retinal image whose linear dimensions are (22mm)/r times those of the patch. Absorption in the eye is ignored. Consider one square patch of the wall, 10.0 cm by 10.0 cm, face-on to the eye. A student says: "six metres is three times two metres, so by the inverse square law the patch must look nine times dimmer."
((a)) Find the radiant flux entering the pupil from the patch at each distance.
((b)) Find the area of the retinal image of the patch at each distance.
((c)) Find the irradiance on the retina at each distance.
((d)) State which quantity falls by nine and which does not, and give the verdict on the student's claim.