Question

Two poles are separated by a distance of $3.14\, m$. The resolving power of human eye is $1$ minute of an arc. The maximum distance from which he can identify the two poles distinctly is

• A. 10.8 km
• B. 5.4 km
• C. 188 m
• D. 376 m

Answer 1

The Correct Option is A

Given the lateral separation of the poles $d =3.14\, m$
The resolving power of the eye is
$\theta=1 \min =\pi /(60 \times 180)$ rad
The maximum distance from which poles are distinctly visible is
$D = d / \theta$
$\Rightarrow D =(3.14 \times 60 \times 180) / \pi$
$=10800 \,m =10.8 \,km$

Answer 2

The resolving power \( \theta \) of the human eye is given as 1 minute of an arc, which is \( \theta = \frac{1}{60} \) degrees or \( \theta = \frac{1}{60} \times \frac{\pi}{180} \) radians. The distance \(d\) between the poles is given as 3.14 m. The formula for the maximum distance \(D\) from which the poles can be identified is: \[ D = \frac{d}{\theta} \] Now, first, convert the resolving power of the eye into radians: \[ \theta = \frac{1}{60} \times \frac{\pi}{180} = \frac{\pi}{10800} \, \text{radians} \] Now substitute \(d = 3.14\) m and \( \theta = \frac{\pi}{10800} \) radians into the formula for \(D\): \[ D = \frac{3.14}{\frac{\pi}{10800}} = \frac{3.14 \times 10800}{\pi} = 10.8 \, \text{km} \] Thus, the maximum distance from which the two poles can be identified distinctly is 10.8 km.