The example below assumes that fixation is in the middle of the objects and that the objects are at different distances from the perceiver. The question addressed is, "What length objects will subtend the same visual angle from two different distances?"
A figure representing the determination of visual angle is here.

The example below shows computation of the visual angle subtended when the extent of the stimulus and viewing distance are known.

computing visual angle
Strengths of illusions may differ when stimuli are viewed under different conditions of illumination or from different distances. Researchers who investigate visual perception often use the visual angle measurement rather than dimensions of objects so that they can report a standardized constant size of the proximal stimulus. Description of a distal stimulus extent would need to be stated with the viewing distance for you to know the size of the proximal stimulus (or projection on the retina). Stating the visual angle is a way to directly and simply reference the size of the image on the retina rather than having to include both extent and distance statements.

For instance, if we state a standard for visual acuity, that standard will apply over a range of distances and not just for one distance. Another outcome from using the visual angle is that the measurement is specific to the site at which energy is transduced. We know that stimulation of retinal regions is equivalent if the visual angles are equivalent.

Distal stimuli typically decrease in visual angle subtended with greater depth. Statement of the visual angle makes the size reference independent of distance. Two distal stimuli can subtend the same visual angle if they have different extents. Often it is important for communication to reference what pattern of stimulation occurs on the retina. Therefore, visual angle is a more apt measure than extent of the distal stimulus.

A WWW presentation of stimuli means that people will view the stimuli on various size monitors with varying resolutions, contrast settings, ambient illumination, brightness settings, and color capabilities. These differences can influence what is seen. It might be interesting, and current technology makes it possible, to gather data online about the strengths of illusions in relation to various WWW presentation differences.

The stimuli for this Gallery are created using a Vivitron 1572, 15" monitor running at a resolution of 1024 X 768 pixels for viewing from about 65 cm. Moving toward and away from the monitor screen may prove interesting and informative with many of the stimuli.

Stating the visual angle subtended by stimuli is one way that researchers communicate some of the information about observation conditions. When researchers state the visual angle, correspondence to regions of the eye may be determined. In addition, other researchers then have a standard for replicating or comparing findings about such matters as strengths of illusory effects. The figure above provides three examples of computing visual angles subtended by stimuli.

In the first two examples the horizontal lengths of stimuli which subtend 5 degrees at viewing distances of 30 and 50 cm. are determined. First, an imaginary line is projected from the eye to the stimulus. This line is perpendicular to the viewing plane and it establishes two right triangles. The angles measured at the eye are each 2.5 degrees.

The TAN (Tangent) of 2.5 degrees equals .043. The TAN of an angle equals the length of the side opposite the angle divided by the length of the side adjacent to the angle. Therefore, in the example for the 30 cm. viewing distance, X (opposite side length) = (.043) * (30 cm.) = 1.31 cm. (1/2 the horizontal length of the stimulus). Multiply 2 * X to find the horizontal length of the stimulus which subtends 5 degrees at the 30 cm. viewing distance.

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