Magnifier

Ordinary magnifier

A loupe is an optical system consisting of a lens or several lenses, designed to enlarge and observe small objects located at a finite distance. It is used in many areas of human activity, including biology , medicine , archeology , banking and jewelry , forensics , watch repair and electronic equipment, as well as philately , numismatics and bonistics .

Content

Options

The main parameters of the magnifier are the diameter of the magnifier and the focal length. Typically, magnifiers with a focal length of ~ 2-20 cm are used . Sometimes, instead of the focal length, an optical power expressed in diopters is used .

Ways to use

Traditional (direct)

Direct observation method in a magnifying glass at a distance

Play media file

Video lesson: magnifying glass

The observed object is placed from the magnifier at a distance slightly less than its focal length . Under these conditions, the magnifier will give a direct enlarged and imaginary image of the subject. The rays from the image fall into the eye at an angle greater than the rays from the subject itself. This explains the magnifying effect of the magnifier.

Direct observation method in a magnifying glass near

To increase the field of view, it is recommended to keep the eye not at a distance, but directly near the magnifier (of course, without blocking the lighting). Contrary to popular belief, the magnification factor of the magnifier does not change (and even increases due to a more complete use of the lens tension) - the psychophysiological effect of the seemingly larger increase when observed from a distance arises from the visual contrast between the unexpanded (observed outside the magnifier) and the magnified magnifier parts of an object.

The increase in the traditional way of using a magnifier is:

\Gamma _{d}={{d} \over {F}}

{\ displaystyle \ Gamma _ {d} = {{d} \ over {F}}}

(when viewed from afar)

\Gamma _{d}={{F+d} \over {F}}={{d} \over {F}}+1

{\ displaystyle \ Gamma _ {d} = {{F + d} \ over {F}} = {{d} \ over {F}} + 1}

(when looking close to the magnifier)

Where $F$ ${\ displaystyle F}$ - the focal length of the magnifier, $d$ ${\ displaystyle d}$ - the distance of the best vision (for an adult from 18 to 50 years old about 25 cm) ^[1] ^[2] ^[3] .

Conclusion

When viewed from afar

The angle at which an object of size l is visible from the distance of best vision is:

\alpha \approx \operatorname {tg} \,\alpha ={l \over d}

{\ displaystyle \ alpha \ approx \ operatorname {tg} \, \ alpha = {l \ over d}}

The maximum increase is achieved when the imaginary image of the object goes to infinity. In this case, the object is observed at an angle:

\beta \approx \operatorname {tg} \,\beta ={l \over F}

{\ displaystyle \ beta \ approx \ operatorname {tg} \, \ beta = {l \ over F}}

Hence the magnification factor:

\Gamma _{d}={\beta  \over \alpha }={{l/F} \over {l/d}}={d \over F}

{\ displaystyle \ Gamma _ {d} = {\ beta \ over \ alpha} = {{l / F} \ over {l / d}} = {d \ over F}}

When looking close to the magnifier

With this observation, the optical powers of the accommodated lens and magnifier add up:

D_{\Sigma }=D_{1}+D_{2}={1 \over d}+{1 \over F}

{\ displaystyle D _ {\ Sigma} = D_ {1} + D_ {2} = {1 \ over d} + {1 \ over F}}

The object will be observed at an angle:

\beta \approx \operatorname {tg} \,\beta =D_{\Sigma }l=l({1 \over d}+{1 \over F})

{\ displaystyle \ beta \ approx \ operatorname {tg} \, \ beta = D _ {\ Sigma} l = l ({1 \ over d} + {1 \ over F})}

Hence the magnification factor:

\Gamma _{d}={\beta  \over \alpha }={l({{1/d}+{1/F}}) \over {l/d}}={{F+d} \over F}

{\ displaystyle \ Gamma _ {d} = {\ beta \ over \ alpha} = {l ({{1 / d} + {1 / F}}) \ over {l / d}} = {{F + d } \ over F}}

Reverse

The reverse way to use a magnifier

A larger increase (though due to a significant reduction in the field of view) can be obtained by considering not an imaginary, but a real image formed in front of the eye at the distance of best vision with a magnifying glass held in an outstretched hand. In this case, the image can be seen turned upside down, and the course of the rays resembles that in a microscope with an accommodated lens of the eye as an eyepiece. It should be noted that for this method of use, the magnifying glass must have good optical quality, otherwise the image will have strong distortions . This method is difficult to use farsighted , as well as suffering from presbyopia ("senile hyperopia").

The increase in the reverse way of using the magnifier is:

\Gamma _{r}={{L-F-d} \over {F}}

{\ displaystyle \ Gamma _ {r} = {{LFd} \ over {F}}}

Where $F$ ${\ displaystyle F}$ - the focal length of the magnifier, $d$ ${\ displaystyle d}$ - distance of the best vision $L$ ${\ displaystyle L}$ - the distance at which the magnifier is held.

Reverse use of a magnifier will only be effective if

\Gamma _{r}>\Gamma _{d}\Rightarrow F<{L \over 2}-d

{\ displaystyle \ Gamma _ {r}> \ Gamma _ {d} \ Rightarrow F <{L \ over 2} -d}

that with L = 70 cm and d = 25 cm gives F <10 cm.

Conclusion

Zoom ratio

The angle at which an object of size l is visible from the distance of best vision is:

\alpha \approx \operatorname {tg} \,\alpha ={l \over d}

{\ displaystyle \ alpha \ approx \ operatorname {tg} \, \ alpha = {l \ over d}}

The actual image is at a distance $d$ ${\ displaystyle d}$ from the eye and, accordingly, at a distance $L-d$ ${\ displaystyle Ld}$ from a magnifier.

To achieve this distance, the object itself should be placed behind the lens at a distance $x$ ${\ displaystyle x}$ which can be calculated from the flat lens formula:

{1 \over f_{1}}+{1 \over f_{2}}={1 \over F}

{\ displaystyle {1 \ over f_ {1}} + {1 \ over f_ {2}} = {1 \ over F}}

{1 \over x}+{1 \over {L-d}}={1 \over F}

{\ displaystyle {1 \ over x} + {1 \ over {Ld}} = {1 \ over F}}

{1 \over x}={1 \over F}-{1 \over {L-d}}

{\ displaystyle {1 \ over x} = {1 \ over F} - {1 \ over {Ld}}}

x={1 \over {1/F-1/(L-d)}}={{F(L-d)} \over {L-F-d}}

{\ displaystyle x = {1 \ over {1 / F-1 / (Ld)}} = {{F (Ld)} \ over {LFd}}}

The image size is proportional to the ratio of the distances from the lens to the subject and to the image:

{l' \over l}={f_{2} \over f_{1}}={L-d \over x}={L-d \over ({F(L-d) \over L-F-d})}={L-F-d \over F}

{\ displaystyle {l '\ over l} = {f_ {2} \ over f_ {1}} = {Ld \ over x} = {Ld \ over ({F (Ld) \ over LFd})} = {LFd \ over F}}

l'=l{L-F-d \over F}

{\ displaystyle l '= l {LFd \ over F}}

From here it is easy to calculate the angle at which the image of the object is observed:

\beta \approx \operatorname {tg} \,\beta ={l' \over d}={L-F-d \over F}{l \over d}

{\ displaystyle \ beta \ approx \ operatorname {tg} \, \ beta = {l '\ over d} = {LFd \ over F} {l \ over d}}

Searched increase:

\Gamma _{r}={\beta  \over \alpha }={((L-F-d)/F)(l/d) \over {l/d}}={L-F-d \over F}

{\ displaystyle \ Gamma _ {r} = {\ beta \ over \ alpha} = {((LFd) / F) (l / d) \ over {l / d}} = {LFd \ over F}}

Performance criterion

\Gamma _{r}>\Gamma _{d}

{\ displaystyle \ Gamma _ {r}> \ Gamma _ {d}}

{L-F-d \over F}>{F+d \over F}

{\ displaystyle {LFd \ over F}> {F + d \ over F}}

L>2F+2d

{\ displaystyle L> 2F + 2d}

F<{L \over 2}-d

{\ displaystyle F <{L \ over 2} -d}

Marking Loops

Magnifiers are marked according to the magnification factor, which is calculated according to the direct method when viewed closely, so a 2 × mark (pronounced “two times”) corresponds to F = 25 cm. Typical parameters of magnifiers are shown in the table:

Marking	Focal length, cm	Optical power, dptr	Coeff. SW. when viewed from afar	Coeff. SW. when viewed near	Coeff. SW. in reverse use	Coeff. SW. for reverse use (d = 20 cm)
2 ×	25	four	1,5	2	0.8	one
2.5 ×	16.67	6	1,5	2,5	1.7	2
3 ×	12.5	eight	2	3	2.6	3
4 ×	8.33	12	3	four	4.4	five
5 ×	6.25	sixteen	four	five	6.2	7
7 ×	4.17	24	6	7	9.8	eleven
7.5 ×	3.85	26	6.5	7.5	10.7	12
10 ×	2.78	36	9	ten	15,2	17
12 ×	2.27	44	eleven	12	18.8	21

Classification

There is an Interstate standard of the USSR “GOST 25706-83. Magnifiers. Types, basic parameters. General technical requirements ”(1983) ^[4] , which was adopted in 1984 and continues to operate in Russia . According to this GOST, they are distinguished depending on the value of the main parameters of the magnifier:

small
middle and
large increase ;

depending on destination:

viewing ,
measuring
cereal
Sentinel
textile
magnifier for viewing frame and
a through-loop magnifier of the paired movie camera visor .

The tripod magnifier consists of an eyepiece, a stage, screws and a mirror.

In philately

Magnifier is widely used by philatelists . A 3-4x magnifier is enough to examine the fine details of a drawing. To determine the printing methods and forms of a raster , a 10-12-fold magnifier ( textile ) is needed. Basically, philatelists prefer folding magnifiers. Some use binocular surgical loops that are mounted in a visor mounted on the head, which frees the collector's hands ^[5] .


Philatelic loupe and tweezers

The magnifier focuses the light rays of a strong source (for example, the Sun ) on a small area, which can be used in extreme situations for:

making fire;
burning out texts or drawings;
cauterization of wounds;
bonding plastic surfaces by melting;

Notes

↑ Hendel A. Fundamental laws of physics. - M .: Fizmatgiz, 1959.- 284 p. (Retrieved March 2, 2010)
↑ Distance of the best vision on vocabulary.ru (unopened) (inaccessible link) . Date of treatment January 21, 2015. Archived January 21, 2015.
↑ The best vision distance at academic.ru
↑ GOST 25706-83. Magnifiers. Types, basic parameters. General technical requirements. - Instead of GOST 7594-75; enter 1984-01-01. - M .: Publishing house of standards, 2003. - 3 p. (Retrieved June 22, 2009)
↑ Levitas Y. Ya., Basyuk V.M. Robot over the philatelic collection // All about brands / J. Ya. Levitas, V.M. Basyuk. - K .: Advertising, 1975 .-- S. 148. - 238 p. - 30,000 copies. (Ukrainian)

Literature

Magnifier // Philatelic Dictionary / Comp. O. Ya. Basin. - M .: Communication, 1968 .-- 164 p.

Links

Baadke M. Even stamp collectors need the right tools. Magnifying glasses . Refresher Course . Linn's Stamp News (May 29, 2000). Date of treatment June 22, 2009. Archived February 9, 2012.
Klug J. A closer look: magnifiers are indispensable tools for collectors . Refresher Course . Linn's Stamp News (January 26, 2009). Date of treatment June 22, 2009. Archived February 9, 2012.
How to use a magnifying glass (unopened) (inaccessible link) . Precious stones and metals, as well as products thereof; DiamondInfo - An article on jewelry. Date of treatment May 15, 2011. Archived on February 14, 2009.

[1] Hendel A. Fundamental laws of physics. - M .: Fizmatgiz, 1959.- 284 p. (Retrieved March 2, 2010)

[2] Distance of the best vision on vocabulary.ru (unopened) (inaccessible link) . Date of treatment January 21, 2015. Archived January 21, 2015.

[3] The best vision distance at academic.ru

[4] GOST 25706-83. Magnifiers. Types, basic parameters. General technical requirements. - Instead of GOST 7594-75; enter 1984-01-01. - M .: Publishing house of standards, 2003. - 3 p. (Retrieved June 22, 2009)

[5] Levitas Y. Ya., Basyuk V.M. Robot over the philatelic collection // All about brands / J. Ya. Levitas, V.M. Basyuk. - K .: Advertising, 1975 .-- S. 148. - 238 p. - 30,000 copies. (Ukrainian)