The visual angle can be measured directly using a theodolite placed at point .
Or, it can be calculated (in radians) using the formula, .[1]
However, for visual angles smaller than about 10 degrees, this simpler formula provides very close approximations:
If one looks at a one-centimeter object at a distance of one meter and a two-centimeter object at a distance of two meters, both subtend the same visual angle of about 0.01 rad or 0.57°. Thus they have the same retinal image size .
That is just a bit larger than the retinal image size for the moon, which is about , because, with moon's mean diameter , and earth to moon mean distance averaging (), .
Also, for some easy observations, if one holds one's index finger at arm's length, the width of the index fingernail subtends approximately one degree, and the width of the thumb at the first joint subtends approximately two degrees.[2]
Therefore, if one is interested in the performance of the eye or the first processing steps in the visual cortex, it does not make sense to refer to the absolute size of a viewed object (its linear size ). What matters is the visual angle which determines the size of the retinal image.
In astronomy the term apparent size refers to the physical angle or angular diameter.
But in psychophysics and experimental psychology the adjective "apparent" refers to a person's subjective experience.
So, "apparent size" has referred to how large an object looks, also often called its "perceived size".
Additional confusion has occurred because there are two qualitatively different "size" experiences for a viewed object.[3] One is the perceived visual angle (or apparent visual angle) which is the subjective correlate of , also called the object's perceived or apparent angular size.
The perceived visual angle is best defined as the difference between the perceived directions of the object's endpoints from oneself.[4]
The other "size" experience is the object's perceived linear size (or apparent linear size) which is the subjective correlate of , the object's physical width or height or diameter.
Widespread use of the ambiguous terms "apparent size" and "perceived size" without specifying the units of measure has caused confusion.
Joynson, 1949, McCready, 1965, 1985, Baird, 1970
Joynson, 1949, McCready, 1965, 1985
- Baird, J. C. (1970). Psychophysical analysis of visual space. Oxford, London: Pergamon Press.
- Joynson, R. B. (1949). The problem of size and distance. Quarterly Journal of Experimental Psychology, 1, 119–135.
- McCready, D. (1965). Size-distance perception and accommodation-convergence micropsia: A critique. Vision Research. 5, 189–206.
- McCready, D. (1985). On size, distance and visual angle perception. Perception & Psychophysics, 37, 323–334.
- Murray, S.O., Boyaci, H, & Kersten, D. (2006) The representation of perceived angular size in human primary visual cortex. Nature Neuroscience, 9, 429–434 (1 March 2006).
- McCready, D. The Moon Illusion Explained.