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 × 10^{3} 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