In the Landolt-C acuity test, the average threshold for accurately identifying the position of the gap in the C-like character was 0.75mm in size, at a distance of 3000mm. What angle is subtended by the gap at this acuity threshold? Show your working and give your answer in Minutes of arc.

  0.859 minutes of arc

Explanation:

The arc length for a given radius and angle in radians is ...

  s = rθ

So, the angle is ...

  θ = s/r

For the given geometry, the angle in radians is ...

  θ = (0.75 mm)/(3000 mm) = 0.00025 radians

In minutes of arc, this is ...

  (0.00025 radians)(60 minutes/degree)(180 degree/(π radians)

  = (0.0025)(60)(180)/π minutes

  ≈ 0.859 minutes

The angle subtended is about 0.859 minutes of arc.