Parallax is a deceptive change in the relative position of an object with a change in the position of the observer. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances.

By measuring the parallax angle and the distance between the two observation points, it is possible to calculate the distance to the object using trigonometry. This is a special case of triangulation, where given one side and two angles, or one angle and two sides, it is possible to calculate the entire triangle. In parallax measurement the triangle is usually very narrow and long, with a very small base and adjacent angles close to 90°. Therefore, measurements must be made with great accuracy.

Parallax error

The parallax error is due to the fact that the index and the scale of the measuring instrument are located on different planes (the operator’s gaze should always be perpendicular to the scale for a correct measurement). Parallax error is primarily caused by viewing the object at an oblique angle with respect to the scale, which makes the object appear to be at a different position on the scale.

For example, if measuring the distance between two ticks on a line with a ruler marked on its top surface, the thickness of the ruler will separate its markings from the ticks.

If viewed from a position not exactly perpendicular to the ruler, the apparent position will shift, and the reading will be less accurate than the ruler is capable of. In the context of reading a piece of volumetric glassware, such as a measuring cylinder, burette, or volumetric flask, the meniscus should be at eye level otherwise there will be an error in the reading. If the meniscus is above eye level an increased volume measurement will be made, conversely if the eye is above the meniscus then a lower volume reading will be made.

A similar error occurs when reading the position of a pointer against a scale in an instrument such as an analog multimeter. To help the user avoid this problem, the scale is sometimes printed above a narrow strip of mirror, and the user’s eye is positioned so that the pointer obscures its own reflection, guaranteeing that the user’s line of sight is perpendicular to the mirror and therefore to the scale.

The same effect alters the speed read on a car’s speedometer by a driver in front of it and a passenger off to the side, values read from a graticule not in actual contact with the display on an oscilloscope, etc.

Measuring and photographic instruments

If an optical measuring instrument, such as a telescope, microscope or theodolite, is not properly focused, the measuring reticle will appear to shift if the operator moves his eye slightly relative to the instrument. For this reason, it is important to take care of the focus of the instrument and the position of the operator.

Also in non-optical measuring instruments, such as a ruler or an analog electrical instrument, parallax can give rise to reading errors (parallax errors). By shifting one’s point of view the marks on the ruler appear to move relative to the point being measured, just as a pointer appears to move above the graduated scale, with a more consistent effect the greater the thickness of the instrument or the distance of the scale: for this reason it is necessary to observe the instrument from a position perfectly vertical to the instrument itself.

A practical method to reduce the reading error is to place a small mirror on the plane of the graduated scale, below the moving index: in this way, closing one eye, the correct reading will be obtained only when the index and its image on the mirror coincide. The most accurate electrical measuring instruments are in fact equipped with a mirror strip on the scale, and the user must position himself so that the reflected image is hidden by the index itself.

In photography the parallax angle is the angle formed between the optical axis of the lens and the optical axis of the viewfinder (in old biotic SLR cameras like Rolleiflex, Rolleicord). The effect of parallax causes the image of nearby objects seen through the viewfinder to differ from the one taken by the lens and for this reason it happens that in some photos the photographed people remain partially cut off from the scene, classic are the old headless photos or with the subject excessively eccentric compared to the photo. This inconvenience is eliminated in the single lens reflex in which you can see exactly what is photographed (the image for pointing and for shooting are taken from the same lens). In cameras with a Galilean viewfinder this defect cannot be eliminated.

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