1. Use Rayleigh criterion for resolution of the eye

For a circular aperture (pupil), the minimum angular resolution is

$\theta_{\min} = 1.22\frac{\lambda}{D}$

where:

• $\lambda = 500\,\text{nm} = 5\times 10^{-7}\,\text{m}$
• $D = 3\,\text{mm} = 3\times 10^{-3}\,\text{m}$

So,

$\theta_{\min} = 1.22\times \frac{5\times 10^{-7}}{3\times 10^{-3}}$

$\theta_{\min} = 1.22\times \frac{5}{3}\times 10^{-4}$

$\theta_{\min} \approx 2.03\times 10^{-4}\,\text{rad}$

2. Relate angular separation to distance of the dots

If the two dots are separated by

$s = 1\,\text{mm} = 10^{-3}\,\text{m}$

and are at distance $L$ from the eye, then for small angles

$\theta \approx \frac{s}{L}$

For just resolution,

$\frac{s}{L_{\max}} = \theta_{\min}$

Hence,

$L_{\max} = \frac{s}{\theta_{\min}}$

Substitute values:

$L_{\max} = \frac{10^{-3}}{2.03\times 10^{-4}}$

$L_{\max} \approx 4.93\,\text{m}$

3. Choose the nearest option

$L_{\max} \approx 5\,\text{m}$

So the correct option is B.

4. Check each option

• A: $1\,\text{m}$ — too small
• B: $5\,\text{m}$ — correct
• C: $3\,\text{m}$ — smaller than calculated value
• D: $6\,\text{m}$ — larger than resolving limit

Therefore, the dots can be resolved up to approximately $5\,\text{m}$.