Question

Two point white dots are $1mm$ apart on a black paper. They are viewed by the eye of pupil diameter $3mm$ . Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light = $500nm$ ]

• A. $6m$
• B. $3m$
• C. $1m$
• D. $5m$

Answer 1

Answer: (D)

Resolution limit $=\frac{\text{1.22}\lambda }{\text{d}}$
Again resolution limit $=\text{sin}\theta =\theta =\frac{y}{\text{D}}$
$\therefore$ $\frac{y}{\text{D}}=\frac{1\cdot 22\lambda }{\text{d}}$

or $\text{D}=\frac{y\text{d}}{\text{1.22}\lambda }$
or $\text{D}=\frac{\left({\left(\text{10}\right)}^{-3}\right)\times \left(3\times {\left(\text{10}\right)}^{-3}\right)}{\left(\text{1.22}\right)\times \left(5\times {\left(\text{10}\right)}^{-7}\right)}=\frac{\text{30}}{\text{6.1}}\approx 5\text{ m}$ .