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A paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of 50 m. The diameter of the eye-lens of the observer is 2 mm. Which of the following is the least value of d, so that the marks can be seen as separate? The mean wavelength of visible light may be taken as 5000 Å
(a) 1.25 m
(b) 12.5 cm
(c) 1.25 cm
(d) 2.5 mm
(b)
Angular limit of resolution of eye, q = where, d is diameter of eye lens.
Also, if y is the minimum separation between two objects at distance D from eye then
Here, wavelength A = 5000 Å = 5 × 10-7 m
D = 50 m
Diameter of eye lens = 2mm = 2 × 10-3
From eq. (1) minimum separation is
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