An 8 by 56 binocular has objectives of diameter mm and angular magnification ; its…

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

Optics and Photonics, Ch Radiometry and photometry

Problem

An 8 by 56 binocular has objectives of diameter D=56D = 56 mm and angular magnification ∣MA∣=8|M_A| = 8; its exit pupil diameter is D/∣MA∣D/|M_A| (Chapter 2). The true field of view has half-angle 0.40∘0.40^\circ, so the apparent field half-angle at the eye is 88 times that. A birdwatcher uses it in bright daylight with an eye pupil of 2.52.5 mm. Treat the instrument as lossless and unvignetted, air throughout (n=1.00n = 1.00), and use Ω=πu2\Omega = \pi u^2 for narrow cones with uu in radians. ((a)) Find the exit pupil diameter. ((b)) Find the etendue offered at the exit pupil and the etendue the eye accepts. ((c)) Find the etendue wasted, and the fraction of the gathered flux that reaches the retina. ((d)) What objective diameter would deliver all of its etendue to this eye pupil at this magnification?

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