A solar cooker uses a Fresnel lens with focusing cone (that 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 solar cooker uses a Fresnel lens with focusing cone f/1.2f/1.2 (that is, the marginal ray of the image-side cone has sin⁡θ′=1/(2×1.2)\sin\theta' = 1/(2\times1.2)) to concentrate sunlight onto a pot. At ground level, after atmospheric absorption, the direct solar irradiance on a surface facing the Sun is 950 W m−2950\ \text{W m}^{-2} (reduced from the 1361 W m−21361\ \text{W m}^{-2} solar constant above the atmosphere). The Sun's angular half-radius, essentially unchanged by the atmosphere, is 4.65×10−3 rad4.65\times10^{-3}\ \text{rad}. ((a)) Find the Sun's radiance as measured at ground level. ((b)) Find the irradiance at the pot, and state, giving the reason from conservation of radiance, whether a bigger lens of the same f-number could ever exceed this bound. ((c)) Given a luminous efficacy for this ground-level sunlight of 98 lm W−198\ \text{lm W}^{-1}, find the corresponding luminance.

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