Secrets of the Chinese magic mirror replica

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2001 Phys. Educ. 36 102

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Secrets of the Chinese magicmirror replicaSe-yuen Mak and Din-yan Yip

Department of Curriculum and Instruction, The Chinese University of Hong Kong, Shatin,NT, Hong Kong

AbstractWe examine the structure of five Chinese magic mirror replicas using aspecial imaging technique developed by the authors. All mirrors are foundto have a two-layered structure. The reflecting surface that gives rise to aprojected magic pattern on the screen is hidden under a polishedhalf-reflecting top layer. An alternative method of making the magic mirrorusing ancient technology has been proposed. Finally, we suggest a simplemethod of reconstructing a mirror replica in the laboratory.

IntroductionThe ‘Chinese magic mirror’ has become a topicof interest for science educators and teachers inrecent years (Swinson 1992, Tao 1998, Yan 1992).The mirror, cast in bronze, is an ancient artifact thatdates back to the Han Dynasty (206 BC–24 AD).It is magic in the sense that when sunlight ornearly parallel light from a laser shines on thepolished convex surface of the mirror, the patternon the back of the mirror mysteriously appears ona screen in front of the mirror (figure 1). Thisobservation tends to suggest that light from theback of the mirror can be transmitted through thebronze mirror and that a convex mirror can forma real image on the screen. Since the bronzemirrors were first reported some 2000 years ago,the original technique for making them mighthave been lost over the centuries. Using moderntechnology, scientists in some Asian countries,such as China and Japan, have succeeded inmaking replicas of the magic mirror with varyingeffects. A number of hypotheses have been putforward to explain how the mirror works, but thescientific principles involved remain a puzzle tomany physics teachers and students. This articleattempts to examine the validity of some of the

Figure 1. A projected pattern with dark contour lines.

explanations offered against empirical evidence.A most popular theory for explaining the

magic mirror is that there are slight changesin curvature on the reflecting surface that aredependent on the pattern formed on the back(Swinson 1992, Yan 1992) during solidification.

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Secrets of the Chinese magic mirror replica

Diffuse reflection gives riseto dark lines on the screen

Back of mirror

Reflecting surfaceof the mirror

Specular reflection givesrise to a bright light patch

Incident sunlight

Figure 2. An earlier explanation of the projected pattern.

The thicker parts of the mirror form a smoothreflecting surface that gives rise to the brightregions on the screen; the thinner parts, being morenarrow and slightly elevated, give rise to the darkregions (figure 2) (Tao 1998). This mechanism oflight reflection explains (1) how an image of thepattern on the back of the mirror is formed withdark lines on a bright background (figure 1) and(2) why the image is equally sharp for any distanceof the screen but its size increases with the distancebetween the image and the screen.

Two explanations have been proposed toaccount for the differential curvature on thereflecting surface. In making the mirror, moltenbronze is first poured into a mould with the patternof the back of the mirror; the front surface isthen ground and polished to a convex surface.Swinson (1992) suggests that, as the surface ispolished, the thinner parts of the mirror bendslightly inward under stress and experience asmaller scraping force than the thicker parts. Atthe end of the process, the smooth surface hasslight elevations that repeat the pattern on the back.Yan (1992), however, suggests that as the moltenbronze solidifies, the thinner parts cool faster thanthe thicker parts, resulting in the slight elevationson the reflecting surface.

Process of investigationIn order to test the validity of the aboveexplanations, we have examined five magic mirrorreplicas purchased from different sources. Basedon our findings listed below about the natureof the images formed and the structure of themirrors, we conclude that the suggestions made bySwinson and Yan cannot provide a comprehensiveexplanation of the effect of the mirror replica.

(1) Our samples of magic mirrors produceimages that can be divided into three differenttypes of pattern. The simplest pattern is one

Figure 3. A projected pattern with bright contour lines.

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Se-yuen Mak and Din-yan Yip

(a)

(b)

Figure 4. (a) Portrait of Jesus Christ formed on thescreen with Chinese and English words ‘GOD WITHYOU’ on the back of the mirror. (b) The mirror surfaceproducing the portrait of Jesus Christ.

with dark lines standing out against a brighterbackground (figure 1). The second pattern ischaracterized by bright lines showing up againsta darker background (figure 3) (Swinson 1992).Unlike the first pattern, which can be captured bya screen in any position, images of the secondtype need to be focused. That is, in order tocatch the sharpest image, the screen must be

(a)

(b)

Figure 5. (a) Flower patterns on the mirror.(b) Projected pattern of part (a).

held at a certain distance from the mirror. Thethird pattern has dark lines several centimetreslong with full or half-tone patches of area noless than 1 cm2 (figure 4(a)). The size of lightpatch produced by the whole mirror is of thesame order of magnitude as the mirror itself, soby simple proportion the surface structure on themirror should in principle be easily seen by theeye. However, figure 4(b) shows that the oppositeis true. The image formation for the last two typescannot be satisfactorily accounted for by the theoryoutlined in the introduction.

(2) In some mirrors, the figure at the back isdifferent from the pattern projected on the screen(figure 4). This means that the theory of slightelevations on the reflecting surface caused byuneven thickness of the mirror is not applicableto this kind of mirror.

(3) On a plastic mirror surface, an oil-basedfelt-pen drawing will produce a projected patternwith coloured lines against a bright background(figure 5), while indented lines made by a bluntpencil will produce an image with bright lines

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Secrets of the Chinese magic mirror replica

Figure 6. (a) Pencil mark on a PVC plastic mirror sticker. (b) Projected pattern of part (a).

A hidden secondlayer with asurface pattern

To TV monitor

To battery

CCD camera

Incident light

Magicmirrorreplica

Incident ray

Reflected rayfrom thehidden layer

Partially reflected rayfrom the smooth top layer

No more than 1 cm

Figure 7. Imaging a hidden layer under the mirror surface using a CCD camera. The enlarged ray diagram on theright shows light and UV rays scattered by the second layer.

against a darker background (figure 6). Also, apartially frosted region of the reflecting surfacecan produce half-tone dark patches. These simpleexperiments provide clues for us to put forward analternative mechanism of image formation for oursamples of mirror replicas.

(4) As no marks or surface irregularities aredetected on the surface of any of the magic mirrorsexamined, we propose that the image pattern ofa magic mirror has been engraved on a hiddensurface covered by a very thin partially reflectingtop layer.

(5) We find that when dilute acid is droppedonto the reflecting surface of a magic mirror, a verythin surface layer is etched away. This suggeststhat the reflecting surface of the mirror may havebeen electroplated with a very thin layer of alloythat is less acid resistant than bronze.

(6) The hidden layer structure can be imagedusing a CCD camera capable of focusing objectsat near zero object distance (figure 7). To do this,a human hair is attached to the mirror surface forreference and a CCD camera is held a few mmaway from it. The mirror is illuminated by light

P H Y S I C S E D U C A T I O N 105

Se-yuen Mak and Din-yan Yip

Figure 8. Photograph taken from a TV screen showingthe human hair, scratches and engraving on the mirrorsurface and the structure in the second layer.

at a grazing angle. The focus of the camera isadjusted so that a clear image of the hair can beformed on the screen of a TV monitor. Becausespecular reflection occurs on the top surface, mostof the light reflected by this surface will not enterthe camera lens. However, the pixels (Breithaupt1995) in the camera have a sensitivity to light that isabout ten times greater, and a threshold wavelengthabout 0.2 µm shorter, than the unaided humaneye. Any structure on the second layer that canscatter visible or ultraviolet light into the camera,albeit slightly out of focus, will be detected on themonitor screen (figure 8). This method enables usto detect the presence of engraving in the secondlayer for all samples tested and provides rigoroussupport for our hypothesis.

A simple homemade model

Based on our hypothesis, a homemade magicmirror can be readily constructed by students inthe classroom. A plane mirror is used instead of aconvex mirror because a partially reflecting curvedsurface is difficult to obtain. A few drops of waterare placed onto the mirror surface over one of thedrawings shown in figure 5(a). The drawing is thencovered with a partially reflecting silvery plasticfilm (figure 9(a)). The film is pressed firmly ontothe mirror surface by squeezing out the water withthe thumb. The drawing under the film becomesalmost invisible. When the mirror is placed insunlight, the hidden pattern is recovered in theprojected pattern (figure 9(b)).

(a)

(b)

Figure 9. (a) A simple homemade magic mirror (theleft-hand side of the plane mirror). (b) The projectedpattern obtained from the homemade mirror.

How could ancient people make themirror?

This model lends support to our alternativeexplanation for the structure and working of themodern replica of the magic mirror. It is moreplausible and comprehensive than the one given bySwinson and Yan. As we do not have the chance toexamine the original ancient artifact, its structure,method of construction and the quality of imageremain unknown. There are two possibilities. Ifthe original mirror had no layered structure—avery likely situation—the pattern on the mirrorsurface can be seen with the unaided eye. A two-layered structure might not be entirely impossible:engraving the pattern in the inner layer requiredjust a combination of skill, effort and time. Athin layer of natural resin could be used to coat thesurface and the outer layer could be made of a verythin sheet of pure gold.

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Secrets of the Chinese magic mirror replica

A final remarkAlthough the magic mirror replica has not beeneasily accessible outside China in the past, itcan now be ordered via the internet or, ifnecessary, purchased by mail-order from the HongKong Association for Science and MathematicsEducation1. As far as teaching is concerned,the magic mirror not only provides an interestingand challenging demonstration, the ‘what, howand why’ of its mechanism of working can alsobe assigned as a student project for independentinvestigation. In doing this, teachers must have aclear picture themselves of how the magic mirrorreplica is constructed. Thus far, a comprehensiveyet consistent solution is still lacking in theliterature. It is hoped that the analysis given in thispaper can provide readers with a more satisfactorysolution.

The skill of detecting forgery, revealing thelayered structure of archive painting or imagingthe internal organs of a body using different typesof radiation is commonly employed in archeology

1 Address of HKASME: Room 114, 1/F, Po On Court, 15 PoOn Road, Kowloon, Hong Kong.

and the medical profession. Due to the lackof resources, these technological applications areoften mentioned in the classroom at a chalk-and-talk level, or at best limited to a watching avideotape. The method of imaging a pattern ina hidden layer using the CCD camera provides areal live example of using modern technology ina detective investigation that can be carried out ina school laboratory. So a study on the structureof the magic mirror replica and its reconstructionwill bridge the gap in our curriculum aboutthe interactive relationship between science andtechnology.

Received 2 August 2000PII: S0031-9120(01)16063-6

ReferencesBreithaupt J 1995 Understanding Physics for A-level

3rd edn (Cheltenham: Stanley Thornes)Swinson D B 1992 Phys. Teacher 30 295–9Tao P K 1998 Phys. Educ. 33 119–25Yan L Y 1992 Phys. Teacher 30 341–3

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