A square matt painting,

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging

Optics and Photonics, Ch Radiometry and photometry

Problem

1.00\ \text{m}\times 1.00\ \text{m}

, of uniform radiance

L = 50\ \text{W m}^{-2}\ \text{sr}^{-1}

(Lambertian to a good approximation) is photographed by a lossless camera lens of focal length

f = 50\ \text{mm}

(converging) set to

f_\# = 4

. The painting is photographed once from

s_o = 2.0\ \text{m}

and once from

s_o = 8.0\ \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 of Chapter 1, find the image side length and hence the image area at each distance. ((b)) Find the irradiance on the sensor, using the result that a distant Lambertian object gives

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

. ((c)) Find the total flux collected on the sensor at each distance, and show that its ratio between the two distances equals the ratio of the image areas, even though the irradiance itself is the same at both distances.

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