Question

Two trees are 1m apart. Person sees them from a distance of 1km. Will he see the trees resolve?
A) Yes
B) No
C) May be resolve
D) none

Answer 1

We have to remember the value of the resolution power of the human eye that is ${\left( {\dfrac{1}{{60}}} \right)^ \circ }$ by this angle we can analyse the trees are resolve or not. If the person makes the angle between two trees is less than the resolution power of the eye then the trees seem not resolved.
Formula Used:
$\dfrac{{\text{d}}}{{\text{D}}} \geqslant RP$

Complete answer:
In the question mentioned the two trees are 1m apart but the person sees them from a distance of 1km. The ratio of these given values should be greater than or equal to the resolution power of the human eye.
The condition is
$\dfrac{{\text{d}}}{{\text{D}}} \geqslant RP$
d is the distance between two trees.
D is the distance between tree and person.
RP is the resolution power of the human eye.
First we have to write given values
d=1m, D=1km
by substituting we get
$\Rightarrow \dfrac{d}{D} = \dfrac{1}{{{{10}^3}}}$
These given values are in radian form so we have to convert it in degree by multiplying $\dfrac{{180}}{\pi }$.
Now, above equation become
$\Rightarrow \dfrac{d}{D} = \dfrac{1}{{{{10}^3}}} \times \dfrac{{180}}{\pi }$
Put this value in condition
$\Rightarrow \dfrac{1}{{{{10}^3}}} \times \dfrac{{180}}{\pi } \geqslant RP$
We know that resolution power of human eye (RP) is ${\left( {\dfrac{1}{{60}}} \right)^ \circ }$
$\Rightarrow \dfrac{1}{{{{10}^3}}} \times \dfrac{{180}}{\pi } \geqslant {\left( {\dfrac{1}{{60}}} \right)^ \circ }$
By substitute $\pi$ value
$\Rightarrow \dfrac{1}{{{{10}^3}}} \times \dfrac{{180}}{{3.14}} \geqslant {\left( {\dfrac{1}{{60}}} \right)^ \circ }$
By solve mathematically we get
$\therefore \dfrac{{180}}{{3140}} \geqslant {\left( {\dfrac{1}{{60}}} \right)^ \circ }$
Hence the condition is satisfied, so if two trees are 1m apart, a person sees them from a distance of 1km. That person sees the trees resolve.

Hence the correct option is C. that is mentioned as maybe resolve.

Note:
In these types of questions we have to remember the condition of resolution power of the human eye. Students give some attention to conversion that is in this question is radian into a degree. Because of this reason, students may choose the wrong answer. Sometimes the question may ask to find the value of d or D. That time we have to remember the value of the resolution power of the eye.