Two binoculars are compared for daytime birdwatching

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

What an Instrument Can See, Ch Pupils: the aperture of a linear system

Problem

Two binoculars are compared for daytime birdwatching, when the observer's eye pupil is dilated to

3.0\,\text{mm}

: an

8\times 42

(objective diameter 42 mm, magnification 8) and a

10\times 25

compact (objective diameter 25 mm, magnification 10). Someone argues: "the

8\times 42

has an exit pupil of

42/8 = 5.25\,\text{mm}

, more than twice the

10\times25

's exit pupil of

25/10 = 2.5\,\text{mm}

, so in daylight the

8\times 42

view must be

(5.25/2.5)^2 \approx 4.4

times brighter." ((a)) Find the error in this reasoning. ((b)) Compute the correct ratio of daytime brightness (retinal illuminance) between the two binoculars.

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