Visual angle

Visual angle is the angle a viewed object subtends at the eye, usually stated in degrees of arc. It also is called the object's angular size. The diagram on the right shows an observer's eye looking at a frontal extent (the vertical arrow) that has a linear size , located in the distance from point . For present purposes, point can represent the eye's nodal points at about the center of the lens, and also represent the center of the eye's entrance pupil that is only a few millimeters in front of the lens. The three lines from object endpoint heading toward the eye indicate the bundle of light rays that pass through the cornea, pupil and lens to form an optical image of endpoint on the retina at point . The central line of the bundle represents the chief ray. The same holds for object point and its retinal image at . The visual angle is the angle between the chief rays of and . The visual angle can be measured directly using a theodolite placed at point . Or, it can be calculated (in radians) using the formula, . However, for visual angles smaller than about 10 degrees, this simpler formula provides very close approximations: As the above sketch shows, a of the object is formed on the retina between points and . (See visual system). For small angles, the size of this retinal image is where is the distance from the nodal points to the retina, about 17 mm. 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.