A pair of " " binoculars has an objective of diameter and angular magnification

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Interference and diffraction

Optics and Photonics, Ch Fraunhofer diffraction from apertures and gratings

Problem

A pair of "

7\times50

" binoculars has an objective of diameter

D = 50\ \text{mm}

and angular magnification

M = 7

. In daylight the observer's pupil constricts to

3.0\ \text{mm}

. Take

\lambda = 550\ \text{nm}

. ((a)) Find the Rayleigh resolution angle the full 50 mm objective could in principle deliver, in arcseconds. ((b)) Find the diameter of the exit pupil of the binoculars. ((c)) The exit pupil is larger than the observer's daytime pupil, so the eye only accepts a

3.0\ \text{mm}

wide part of the beam; this crops the entrance aperture to an effective diameter

D_{\text{eff}} = (\text{eye pupil})\times M

. Find

D_{\text{eff}}

and the resolution angle actually achieved in daylight.

Related theory

Interference and diffraction

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