Question

Binoculars featuring an objective lens with a diameter D = 45 mm are used in daylight. Find the maximum useful magnification and the exit pupil diameter assuming 1 arcmin for the angular resolution of the eye at the wavelength of light λ = 0.55 µm

Answer 1

Diameter of the objective lens = 45 mm

Angular resolution = 1 arcmin = ( 1× π )/(180×60) = 2.91 × 10 -4 rad

Wavelength of the light = 0.55 × 10 -6 m

Angular resolution = (1.22 ) / De

Diameter of the exit pupil De = (1.22 )/

De = (1.22× 0.55 × 10 -6)/ (2.91 × 10 -4)

De = 2.306 × 10 -3 m

Magnification = (object size / image size )

Magnification = (45 ×10 -3) /(2.306 × 10 -3)

Magnification = 19.5

Diameter of the exit pupil = 2.3 mm

Magnification = 19.5