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Magnification ofconvexlensis positive or negative

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This means that object can be seen in the same size as if observer comes close to it in 1/γ distance. As magnification gets bigger, the structure becomes bigger as well as viewable range becomes narrower and image becomes darker because “exit pupil” becomes smaller. Binoculars with specifications of 6 to 8-foldmagnification and 30 – 42 mm in diameter2 is manly used for bird watching for its portability. While that with specifications of 7 – 18-foldmagnification and 50 – 70 mm in diameter is mainly used for star watching. Binoculars of high magnification are usually used with tripod to mount. Meanwhile, that of around 10-foldmagnification with stabilizing mechanism is getting popular for theater use recently. Exit pupil is calculated with formula as “lens diameter ÷ magnification”, and it get hard to see if it is smaller than eye pupil. Because of this reason, binoculars with exit pupil of more than 3 mm are used in daytime, and that with more than 5 mm is used in nighttime or dark place. Binoculars with compact size and high magnification are sold as popular type. Due to smaller exit pupil, their view might be dark or visibility might be lost by eye movement (black out). Careful use is required for these types of binoculars.

Lensformula

Let “permissible circle of confusion CoC” be larger one of “pixel pitch Ppix” or “airy disk diameter Dairy”. “Depth of field DoFi” can be found with dividing “depth of focus DoFo” by “longitudinal magnification α”.

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Ratio of length change by optical system is called “magnification”. Taking lenses used in photo or machine vision are included in “Image forming optical system”. In the term of “magnification m”, there are “lateral Magnification β” and “longitudinal magnification α”. β indicates ratio in size of concerned object and image while α indicates ratio in optical axis. These will be explained in next chapter. In case of magnification in size, it is called “equal magnification”, “1-fold magnification” or “1x” if image and object are the same in size. The value is more than1 such as “2-fold magnification”, “2 power” or “2x” in case of expansion while it is less than 1 such as “0.5-fold magnification” or “0.5x” in case of shrinking. Furthermore, the sign of magnification (Lateral magnification, β) is negative (-: minus) as image is usually inverted.

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Magnification of a lenscalculator

Magnificationformula forlensin termsoffocal length

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As taking lens in image forming optical system shoots real image, “Lateral magnification β”, size ratio, can be calculated by direct measurement of object and image. On the other hand, in case of tele scope and binoculars, real image made by objective lens is seen as virtual image through eyepiece. They are in a special optical system as incident light and outgoing light is parallel to optical axis. In this optical system, called “afocal system” or “no focus optical system”, “angular magnification γ”, which is a ratio of inclination angle u’ between light from object and optical axis to inclination angle u’between light to image and optical axis, is used for magnification m.1

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According to this formula, the smaller the F number (brighter) of lens, the smaller the pixel pitch of sensor and the larger the optical magnification (enlargement) the narrower the depth of field. Incidentally, “depth of field DoFi” is applicable to short object distance case such as machine vision, however, the depth is significantly different between the front side and the back side of the object in long object distance case such as surveillance camera. In this case, “depth of field DoFi” is found with “depth of focus DoFo” and “Newton’s lens formula”3.

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Magnification of a lensformula

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In the machine vision field, optical magnification is important to select taking lens or to consider optical system. However, it is not well known and sometimes confused that magnification has a meaning other than imaging magnification, generally known, which indicates size ratio of object and image. We would like to explain, here, a concept and applications of magnification clearly.

Therefore, longitudinal magnification α is the square of lateral magnification β in case amount of object movement is comparatively small.

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”Longitudinal magnification α” is a ratio of “minute transfer amount ⊿x’” of image against “minute transfer amount ⊿x” of object along optical axis. In other words, it means sensitivity on focus out.

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Magnification ofconvexlens

In case of zoom lens, used in digital camera or video camera, magnification of 3x, 6x or 30x are indicated. This is called “zoom ratio” and it means ratio between focal length of longer side (tele side) and shorter side (wide side). For example, zoom ratio of zoom lens which focal length can be adjusted 8 – 80 mm is 10x.

“Distance of distinct vision” is the distance between eyes and object in which we can see the object clearly without tension or fatigue. It is supposed to be 250 mm (=4 diopter) since ancient age. The reason that 25 – 30 cm distance is recommended for book reading is also distinct vision distance. By the way, elasticity and adjustability of eye lens is getting lower as aging and object can hardly be seen unless locating it further than distance of distinct vision. This is so called Presbyopia.

Magnifying glass is also in optical system to see virtual image. Magnification m can be calculated as a ratio of “distance of distinct vision of 250 mm” and “focal length of f”.

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Millimeters to Pixels Conversion Table ; 16.5mm, 62.3622px, 194.8819px ; 17mm, 64.252px, 200.7874px ; 17.5mm, 66.1417px, 206.6929px ; 18mm, 68.0315px, 212.5984px.

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In case of general object distance in machine vision, the formula can be easily found with above mentioned “longitudinal magnification α” because “depth of field DoFi” is “depth of focus DoFo” which is shifted to object side through lens.