Question

A person wishes to distinguish between two pillars located at a distance of $11\mathrm{km}$. What should be the minimum distance between these pillars (resolving power of the normal human eye is $1\text{'}$)?

• A. $1\mathrm{m}$
• B. $3.2\mathrm{m}$
• C. $0.5\mathrm{m}$
• D. $5\mathrm{m}$

Answer 1

The correct option is B

$3.2\mathrm{m}$

Step 1. Formula of angular resolving power of human eye.

The angular resolving power of human eye is the inverse of resolving limit.

The resolving limit is minimum angular separation between two object, so they can just resolved.

For human eye, resolving limit is $\frac{1}{60°}$.

Resolving power $\mathrm{\theta }=\frac{1}{60}\times \frac{\mathrm{\pi }}{180}$ in radians.

$=\frac{3.14}{10800}$ radian

Step 2. Determine the minimum distance between two pillars.

It is given that the a person wishes to distinguish between two pillars located at a distance of $11\mathrm{km}$.

So, the Distance of pole from a person is $11\mathrm{km}=11000\mathrm{m}$.

As we know that,

$\mathrm{\theta }=\frac{\mathrm{arc}}{\mathrm{radius}}$

Let,

arc $=\mathrm{x}$ (minimum distance between pillars)

radius $=11000\mathrm{m}$ (distance of pole from man)

Put the values in the above formula, we get,

$\mathrm{\theta }=\frac{\mathrm{x}}{11000}$

$\frac{3.14}{10800}=\frac{\mathrm{x}}{11000}$

$\mathrm{x}=3.2m$

So, the minimum distance between two pillars is $3.2\mathrm{m}$.

Hence, the option $\mathrm{B}$ is correct answer.