A plano-convex lens of clear aperture diameter m and f-number (so its focal length is…
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 plano-convex lens of clear aperture diameter D=0.20 m and f-number f#=1.2 (so its focal length is f=f#D=0.24 m) is used as a small solar furnace, focusing sunlight to a spot at its focal plane. The Sun's full angular diameter as seen from the Earth is 9.30×10−3 rad (twice its half-angle of 4.65×10−3 rad), and the solar constant is 1361 W m−2. Treat the Sun as a small, uniform Lambertian disc and the lens as lossless; take the focal-plane image of the Sun to be a simple geometric image of angular size 9.30×10−3 rad.
((a)) Find the diameter, and hence the area, of the Sun's image at the focal plane.
((b)) Find the total radiant power entering the lens's aperture from the Sun.
((c)) Find the Sun's radiance, and hence the irradiance delivered to the focal-plane image.
((d)) Multiply your answers to (c) and (a) to find the power delivered to the image, and check that it agrees with (b). Explain, in one sentence, why this agreement is expected for a lossless system.