visual angle

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The angle subtended at the nodal point of the eye's crystalline lens by a visual stimulus, determined jointly by the size of the stimulus and its distance from the observer. The visual angle subtended by the moon in the night sky is almost exactly one-half of a degree or 30 minutes of arc, this being the angular size of the stimulus. Labelling the visual angle θ (degrees), if the linear size (height, width, or diameter) of the stimulus is h and its distance from the observer is d, where h and d are measured in any units provided they are the same, then according to simple trigonometry tan (θ/2) = (h/2)/d. Hence for the image of a person 6 feet tall at a distance of 100 feet, h = 6, d = 100, and tan (θ/2) = 3/100 = 0.03. Using an inverse tangent button (tan−1) on a pocket calculator or a table of tangents, we can determine that θ/2 = 1.72, therefore the visual angle θ subtended by the object is 3.44 degrees or 3 degrees and 26 minutes of arc. For small visual angles, the approximation tan θh/d may be used, yielding in this example tan θ = 0.06 and θ = 3.43 degrees, which also rounds to 3 degrees and 26 minutes of arc. The moon's diameter is 2,160 miles and its average distance is 238,900 miles, therefore tan θ ♠ 2,160/238,900, yielding an angular size of θ ♠ 0.52. The sun's diameter is approximately 400 times that of the moon and it is 400 times further away, so by a remarkable coincidence, it subtends almost exactly the same angle at the eye. See also Aubert-Förster phenomenon, Emmert's law, König bars, minimum separable, minimum visible, size constancy.

Subjects: Psychology.

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