Question

Two parallel pillars are 11km away from an observer. the minimum distance between the pillars so that they can be seen separately wwilll be -

Answer 1

For the eye to distinguish between two objects clearly and separately, the angular separation of two distant objects at the eye should be >= 0.0002 radians. That means 0.01146°  or  0.687 ' 

Let the separation = x  meters

angular separation = x/11000  = 0.0002   rad
=> x = 2.2 meters   approximately.

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The minimum angular separation is the diffraction limit of the width of the pupil. It is given by  Ф ≈ 1.22 * λ / D
where  λ = wavelength of the light rays
            D = diameter of the pupil (≈4mm)

Answer 2

The minimum angular separation between two distinct objects can be identified if the angle between them is greater than (1/60)°

If the distance between the two objects is d and the distance between the objects and the observer is x then

d/x>(1/60)°×π/180

d>(π×x)/(60×180)

In the question the x is given as 11km=11000m

d>(3.14×11000)/(60×180)

d>3.2m