A matt studio wall is uniformly lit and behaves as a Lambertian surface of luminance cd m
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 matt studio wall is uniformly lit and behaves as a Lambertian surface of luminance Lv=250 cd m−2. All of the wall is covered with black cloth except one face-on square patch of area 0.25 m2. Two instruments are pointed at the patch, both from 2.00 m and then from 8.00 m: a bare photocell, facing the patch, which reads the illuminance falling on its own front face; a light meter whose lens of focal length 30 mm works at f/2.8 and reads the illuminance in the image it forms of the patch. Both object distances are large compared with the focal length, so the distant-object form of the image illuminance may be used. The lens is lossless and unvignetted.
((a)) Find the illuminance on the bare photocell at each distance.
((b)) Find the illuminance in the image inside the light meter at each distance.
((c)) A student concludes from (a) that the wall must be photographed with a longer exposure from 8.00 m than from 2.00 m. Say what is wrong.