Q: A man wants to distinguish between two pillars located at a distance of 11 km. What should be the minimum distance between the pillars ?
Sol: As the limit of resolution of human eye is
$\displaystyle \theta = 1′ = (\frac{1}{60})^o $
$\displaystyle \theta = \frac{\pi}{60 \times 180} $
If x is minimum distance between the pillars,
and d = 11 km = 11 × 103 m ,
then from $\displaystyle \theta = \frac{x}{d} $
$\displaystyle x = d \times \theta $
$\displaystyle x = 11 \times 10^3 \times \frac{\pi}{60 \times 180} $
x = 3.2 m