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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.

1. 1.25 m
2. 12.5 cm
3. 1.25 cm
4. 2.5 mm

Correct answer: 2.5 mm

Solution

The resolving power of the eye is determined by the Rayleigh criterion, which states that the minimum angular separation θ = 1.22 * (λ/D), where λ is the wavelength of light and D is the diameter of the eye lens. Using θ = d/50, we solve for d and find it to be 2.5 mm.

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