Q 12-10-009JEE MainAIEEE 2005Medium
Two point white dots are $1$ mm apart on a black paper. They are viewed by an eye of pupil diameter $3$ mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light $= 500$ nm]
Answer: (C) $5$ m
Limit of resolution of the eye: $\theta = \dfrac{1.22\lambda}{D} = \dfrac{1.22 \times 500 \times 10^{-9}}{3 \times 10^{-3}} \approx 2.03 \times 10^{-4}$ rad.
The dots are just resolved when $\dfrac{1\ \text{mm}}{x} = \theta$:
$$x = \frac{10^{-3}}{2.03 \times 10^{-4}} \approx 4.9\ \text{m} \approx 5\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics