A solid glass light pipe of refractive index has an input face of area and accepts…

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

What an Instrument Can See, Ch Radiance, etendue and a throughput budget that is spent

Problem

A solid glass light pipe of refractive index n=1.5n=1.5 has an input face of area A=10 mm2A = 10\ \mathrm{mm}^2 and accepts light out to a half-angle θ=60∘\theta = 60^\circ inside the glass. ((a)) Compute the exact etendue Ξ=πn2Asin⁡2θ\Xi = \pi n^2 A \sin^2\theta. ((b)) Compute the paraxial approximation Ξpar=πn2Aθ2\Xi_{\mathrm{par}} = \pi n^2 A \theta^2, with θ\theta in radians. ((c)) By what percentage does the paraxial formula overestimate the exact value?

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