Resolution of the eye

1. The problem statement, all variables and given/known data
The pupil of the human eye is normally around 5mm in diameter. A person with 20/20 vision
should be able to read letters 9mm high at a distance of 20m, while in Chapter two of
The Two Towers Legolas can resolve objects of around 10cm size at a distance of five leagues
(about 24km). Comment

2. Relevant equations
The Rayleigh resolution limit for a circular aperture (assuming small angles is) θ=1.22λ/w where w is the diameter of the aperture.

3. The attempt at a solution
Ignoring the second part for now, using the above equation, we can resolve two point objects by eye when their angular separation is 0.0001342rad.
I have assumed λ=550nm for visible light.

A letter 9mm high at a distance of 20m subtends an angle given by θ=9/20000=0.00045rad at the eye.

Now these angles are of the same order which seems to indicate I’m going in the right direction. However I can’t quite work out what I should exactly do with them next because:
– I don’t know the separation of two letters, only the height of a single letter.
– The letters aren’t actually point objects.

Any clues? Thanks.

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