A matt chalkboard

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 chalkboard,

1.00\ \text{m}

high by

1.20\ \text{m}

wide, of uniform radiance

L=40\ \text{W m}^{-2}\ \text{sr}^{-1}

(Lambertian) is photographed by a lossless converging lens of focal length

f=85\ \text{mm}

set to

f_\#=2.8

, once from

s_o=1.5\ \text{m}

and once from

s_o=6.0\ \text{m}

. Use the real-is-positive sign convention:

s_o>0

for the real object,

s_i>0

for the real image. ((a)) Using the thin lens equation, find the image area at each distance. ((b)) Find the sensor irradiance using

I_{\rm image}\approx \pi L/(4f_\#^2)

. ((c)) Find the total flux collected on the sensor at each distance, and compare the ratio of fluxes with the ratio of image areas.