Question

A person wants to resolve two thin poles standing near each other from a distance of $2\mathrm{km}$. The distance between the pillars must be approximately

• A. $0.25\mathrm{m}$
• B. $3.2\mathrm{m}$
• C. $1\mathrm{m}$
• D. $0.5\mathrm{m}$

Answer 1

The correct option is D

$0.5\mathrm{m}$

Step 1: Given data

Distance of pole from a person is $2\mathrm{km}$.

We have to find the approximate distance between two pillars.

Step 2: Formula to be used

As we know, the angular resolving power is the inverse of the resolving limit.

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

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

Step 3: Evaluate the formula according to the given situation

Let,

The separation between two pillars $=\mathrm{xm}$

Distance of pole from a person is $2\mathrm{km}=2000\mathrm{km}$.

Limit of resolution $\mathrm{\theta }=\frac{1}{60°}$

$=\frac{1}{60}\times \frac{\mathrm{\pi }}{180}$ in radian

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

Step 4. Determine the approximate distance between two pillars.

We know that,

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

From the given,

Arc $=$ separation between two pillars

Radius $=$ Distance of pole from a person

So,

$\frac{\mathrm{x}}{2000}=\frac{3.14}{10800}$

$\mathrm{x}=0.58$

Therefore, the approximate distance between two pillars is $0.5\mathrm{m}$.

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