Parallax localization of a virtual image matches the apparent depth of a virtual image to a directly viewed physical marker. A sideways change of viewpoint changes their relative apparent positions if their depths differ. Adjust the marker until that relative motion vanishes, and use its coordinate to estimate image position. The marker must be viewed directly; viewing it through the same optical lens compares two images rather than an image and a known physical depth. [ref].
For two nearly aligned points at distances from an eye displaced sideways by , the small-angle approximation gives a change of relative viewing angle proportional to . It vanishes when , and changes sign across that match. When both distances are large, the difference is small, explaining the poor depth precision near the thin lens condition .
Virtual image 2026-10-14
A virtual image is the apparent origin of an outgoing diverging bundle: the backward extensions of its light rays intersect at the image point. Those extensions are geometric constructions, not backward-travelling light. A screen placed there cannot intercept the outgoing bundle to display that virtual image. An eye or a second optical lens receiving the actual outgoing light rays can nevertheless form a subsequent real image. “Virtual” describes this imaging stage, not whether the image can be seen or photographed. [ref].
For a converging thin lens with , the same equations give and : the virtual image is upright and enlarged. For the illustrative choice , , ,
The image appears farther from the optical lens than the object. A diverging thin lens with a real object instead has and , so a virtual image need not be enlarged. A plane mirror provides another virtual image, located behind the reflecting surface by backward extensions of the reflected light rays. [ref].
Figure 1.
Backward ray extensions locate a virtual image; gives parallel outgoing light rays
. Original ideal-model diagrams for a converging thin lens with and . Above, solid light rays travel rightward while dashed backward extensions meet at . Below, each object point at sends out a parallel bundle, so there is no finite image position. Vertical distances are enlarged; both panels share coordinate scales. These are predictions, not measurements. Details.
For a direct viewing test, bring the target to , search for a sharp screen image on the outgoing side, then remove the screen and look through the optical lens toward the target. Expect an upright enlarged view if the eye receives the bundle and can focus. Record the eye position: beyond the optical lens gives a predicted apparent distance . This adapts the Northern Virginia laboratory's comparison. [ref].
For a position measurement, use parallax localization of a virtual image. Place a movable pencil tip or narrow comparison marker beside the apparent image, and view that marker directly beside or above the optical lens, while viewing the image through it. Move the head a little sideways and move the marker along the bench until relative lateral motion vanishes. Read its coordinate ; the estimate is . Deliberately place the marker nearer and farther to check that relative motion reverses on opposite sides of the match. This follows Orhan Aytür's lens laboratory, which uses a pencil to locate a virtual image. [ref].
Keep target and optical lens fixed, use one eye and the central image detail, and ensure the marker itself is not viewed through the optical lens. A marker blocked by the target, or a head movement that loses the bundle through the aperture, invalidates that trial. Repeat the match from both directions and record its depth range. This measures apparent depth; comparing apparent sizes at different depths does not directly measure transverse magnification. Near , apparent depth becomes very large and the match is poorly constrained. A failed screen search alone therefore needs the distance check and the viewing test.