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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.
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- 1.25 m
- 12.5 cm
- 1.25 cm
- 2.5 mm
Correct Option: B
Angular limit of resolution of eye,
| θ = | d |
where, d is diameter of eye lens. Also, if y is the minimum separation between two objects at distance D from eye then
| θ = | D |
| ⇒ | = | ⇒ y = | .....(1) | |||
| D | d | d |
Here, wavelength λ = 5000 Å = 5 × 10-7m
D = 50 m
Diameter of eye lens = 2 mm = 2 × 10-3m
From eq. (1), minimum separation is
| y = | = 12.5 × 10-3 m = 12.5cm | 2 × 10-3 |
