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
Concept. The dots are resolved while the angle they subtend exceeds the eye's limit $\dfrac{1.22\lambda}{D}$.
Step 1. Limit of resolution.
$$\theta = \frac{1.22 \times 500 \times 10^{-9}}{3 \times 10^{-3}} \approx 2.03 \times 10^{-4}\ \text{rad}$$
Step 2. Maximum distance. $x = \dfrac{10^{-3}}{2.03 \times 10^{-4}} \approx 4.9$ m $\approx 5$ m.
Answer. $5$ m (Option C).
Solution by Sreeraj P, M.Sc Physics
