Question

The resolution limit of eye is $1min.$ At a distance $xkm$ from the eye two persons stand with a lateral separation of $3m.$ For the two persons to be just resolved by the naked eye, $x$ should be,

• A. $10km$
• B. $20km$
• C. $15km$
• D. $30km$

Answer 1

Answer: (A)

$\theta =1min={\left(\frac{1}{60}\right)}^{\circ }=\frac{1}{60}\times \frac{\pi }{180}=\frac{\pi }{10800}rad$

$\theta =\frac{3\times 10^{-3}}{x}$
$x=\frac{3\times 10^{-3}}{\theta }=\frac{3\times 10^{-3}}{\frac{\pi }{10800}}\sim eq10Km$