Question

The resolution limit of the eye is $1^{\prime }$. At a distance $xkm$ from the eye, two persons stand with a lateral separation of 3 meter. For the two persons to be just resolved by the naked eye, $x$ should be:

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

Answer 1

The correct option is A $10km$

Distance = $xkm=1000xm$

Resolution limit $=1^{\prime }$

Lateral separation $=3$ meter

Angle on eye in minutes for 2 person, $x$ km away separated by $3$ meter $=$ $\frac{3}{1000x}\times \frac{180}{\pi }\times 60$

So, $1=$ $\frac{3}{1000x}\times \frac{180}{\pi }\times 60$

$\Rightarrow x=10.3$ Km ( approximately $10$ Km)

Answer. A) $10$ Km