Several viewpoints of Chinese and foreign scholars
Metal cannot transmit light. Why is this kind of bronze mirror called transparent mirror, the sun shines on the mirror, the reflected light hits the wall, and there is a pattern on the back of the mirror? How is it made?
Scholars at home and abroad have put forward various hypotheses, which can be summarized into two views:
1. Due to the different tissue structure or composition, each point on the mirror surface has different light reflectivity, resulting in different bright shadows;
2. Due to the unequal concave-convex curvatures, the reflection of light at each point of the mirror surface is inconsistent, resulting in different bright shadows.
If we observe the mirror structure, we can find that it has a certain relationship with the thickness of the mirror. The thin part of the mirror body (without ornamentation) has fine texture and no obvious α primary crystal; In the thick part (with decorative patterns on the back of the mirror), the grains are coarse and there are obvious α primary crystals. Is this difference in mirror structure the reason why ancient mirrors transmit light? There was a bright white film on the surface of the transparent mirror in the Western Han Dynasty, which covered the whole mirror, that is, the original differences of these structures on the mirror were covered by this film and could not be revealed in the sun. It can be seen that the light transmission of the transparent mirror in the Western Han Dynasty has nothing to do with the mirror structure.
In order to further understand the relationship between the difference of mirror structure and the light transmission phenomenon, a layer of zinc sulfide transparent layer and a layer of gold were plated on the mirror surface of the self-made light transmission mirror, and the results still showed the light transmission effect. If vacuum coating is used to coat a layer of aluminum or silver on the mirror surface of the self-made "transparent mirror", it will also show the effect of light transmission. In addition, if there are differences in microstructure and grains due to different thicknesses, light transmission will occur, then the greater the thickness difference or even the difference, the better the light transmission effect. But in fact, almost all bronze mirrors, especially Tang mirrors, have raised patterns on the back, and some of them vary greatly in thickness. However, so many bronze mirrors are opaque. So this explanation is not in line with the actual situation.
So, is the light transmission of the transparent mirror in the Western Han Dynasty due to the different concave-convex curvatures of the mirror? It can be considered that the Japanese magic mirror transmits light because of the different concave-convex curvature of the mirror surface, and the light transmission effect of the Western Han mirror is not the same as that of the Japanese magic mirror. When the Japanese mirror reflects light, its image is clearly displayed on the screen only in a short distance, and beyond a certain distance, the reflected image becomes blurred; However, with the increase of reflection distance, the brightness of the image gradually weakens, but the light and dark parts gradually increase. Also, some specular reflections are hollow, that is, the edge of the pattern is bright and the center is dark. The images reflected by the transparent mirror in the Western Han Dynasty are bright and three-dimensional.
Judging from several transparent mirrors collected by Shanghai Museum, their * * * features are as follows:
1. There are wide and thick edges around the mirror body:
2. The mirror body is very thin, only 0.5 ~ 0.9mm；;
3. The mirror surface is slightly convex, the back of the mirror corresponds to the curvature of the mirror surface, and the thickness of the whole bronze mirror is relatively uniform except for the ornamentation;
4. There are raised decorative patterns arranged along the circumferential direction on the back of the mirror, but there are no raised lines perpendicular to the circumference.
Residual stress is the basic factor of light transmission of copper mirror.
It is precisely because of these characteristics of the transparent mirror in the Western Han Dynasty, and because the mirror body of the bronze mirror is thin, it cools quickly in the casting process; The mirror ring is thick and slow. When the mirror ring is still condensing and shrinking, the mirror body has solidified and has certain rigidity. At this time, the contraction of the mirror ring plays a firm role in the mirror body. At the same time, the cured mirror body also supports the mirror ring. After the bronze mirror is cold-fixed, the relationship between the acting force and the reaction force between the mirror body and the mirror ring is shown in Figure 2.
When the mirror body is subjected to radial pressure P and bending moment M(M=RMt), residual stress will be generated in the mirror body. Because the mirror is convex, under the action of residual stress, the mirror tends to arch. However, the mirror body has a certain rigidity. Only when the mirror body is thinned to a certain extent and the bending stiffness has been obviously reduced, the radial pressure and bending moment will deform the mirror body and obviously arch to the mirror side. The thickness of the mirror varies from place to place (thicker with ornamentation, thinner without ornamentation, and the rigidity of the thin part is less than that of the thick part. When the mirror is arched, the deformation of the thin part is greater than that of the thick part, that is, the protrusion of the thin part is greater than that of the thick part. This forms a fully convex mirror surface with different degrees of protrusion everywhere on the mirror surface of the light-transmitting mirror. When the bronze mirror is ground, the stiffness of the mirror body is decreasing at different rates, and the deformation difference of the mirror body is getting bigger and bigger. The difference of mirror curvature is more and more obvious, and it becomes a more uneven mirror. This difference in mirror curvature corresponds to the decorative pattern on the back of the mirror, so the image of alternating light and dark reflected by sunlight is the image of the back of the mirror. Fig. 3 is an enlarged schematic view of the mirror surface.
The laser interferogram can further prove the above viewpoint. The mirror surface of the transparent mirror is fully convex, and the curvature radius of the mirror surface without decoration is smaller, while the curvature radius of the mirror surface with decoration is larger. In fact, the potential difference caused by curvature is too small, and the fluctuation is only a few microns, which is imperceptible to the naked eye, and can only be seen in the reflected image after being amplified by the optical path. As can be seen from Figure 3, the curvature of thick places with inscriptions is small, and the curvature of thin places without inscriptions is large. When the parallel light hits the mirror, the reflected light scatters in the place with large curvature, and the projection on the screen is dark, while the reflected light is concentrated in the place with small curvature, and the projection is brighter than the reflected light of the mirror with large curvature around it, so there is a bright solid handwriting pattern in the reflected image, which is the mystery of light transmission.
The image of Japanese magic mirror is hollow because it uses scraping method. The edge of the handwriting is where the thickness meets. When scraping, the force is the greatest, and the mirror surface will produce corresponding concavity, and the reflected light is particularly concentrated. It can be seen that both the transparent mirror of the Western Han Dynasty and the magic mirror of Japan have light transmission, but the principle of light transmission is not exactly the same.
The curvature difference caused by residual stress makes the bronze mirror transparent. Not only the curvature calculated by mechanical theory is consistent with the measured value, but also it can be verified by another experiment. That is to break the transparent mirror on the ground, or chisel off the mirror ring, that is, separate the mirror ring from the mirror body to release the residual stress, and you will find that the mirror body is no longer opaque. Another simple experiment can also confirm the above point of view, that is, to grind off the individual handwriting of the transparent mirror, that is, to reduce the thickness of the thicker part to the same thickness as the thin part. According to the above theoretical analysis, the milled thin place will arch evenly as the original thin place, and the curvature change is consistent, so it should not transmit light again, and the result is expected.
In order to further prove the role of residual stress caused by bending moment, a simple experiment can be done. When the sun shines on the transparent mirror, hold the mirror ring with four fingers and use the thumb mirror button at the same time. As a result, we can find that the transparency effect is better.
To this end, another experiment was done. The copper mirror is placed in a ring with the same diameter as the mirror ring (see Figure 4), and a load Q is applied to the center of the copper button. The radial and circumferential strain values are measured on the mirror surface opposite to the thick and thin parts of the mirror back respectively. It can be seen that with the increase of load, the strain value of thin-walled part increases much faster than that of thick-walled part. In flexural members, strain varies with curvature, that is, the strain value directly reflects curvature. The strain can be measured, and the stress can be calculated through the strain, from which the calculation relationship between stress and curvature can be deduced. Although this loading mode is not exactly the same as the actual load of the mirror, it can at least be said to be a simulation test of additional bending moment, reflecting the simulated residual stress on the mirror. After q loading, the light transmission effect of copper mirror is improved. Such experimental results intuitively reflect that the curvature difference between the thick and thin parts of the mirror can be increased under the action of bending moment within the elastic range, which proves again that the above theoretical analysis is in line with the facts.
Some people will ask this question: it has been more than two thousand years since the transparent mirror of the Western Han Dynasty, and the residual stress can be maintained for so long, and the transparent mirror still has the effect of light transmission. According to the physical properties of metals, the residual stress will decrease with time, but after a period of time, the release of residual stress will decrease to a certain value with little change. More importantly, the original elastic deformation under stress has been transformed into plastic deformation and fixed, that is to say, the deformation of the bronze mirror and the curvature difference everywhere have been preserved.
Polishing is an important link in the light transmission of bronze mirrors.
Since the mirror defects of the same structure in the Western Han Dynasty have casting residual stress, do these mirror defects have light transmission effect as long as they are thinned to a certain time? In fact, the same mirror is polished in different ways, so it can be divided into transparent and opaque. For example, when the grinding force is uneven, the stress on the mirror surface is uneven everywhere, and the grinding degree varies from place to place. In some places, it is too thin to wear any more, and in some places, it is not thin enough to transmit light. Of course, it cannot achieve the effect of transmitting light. However, if the correct grinding method is adopted, the mirror surface will be ground on the grinding disc. When the thickness and stiffness of the mirror body are small to a certain extent, the mirror surface will obviously arch, resulting in poor curvature of the mirror surface, thus having a light transmission effect.
However, after it was found that the light-transmitting mirror was broken, as mentioned above, some light-transmitting mirrors were no longer light-transmitting. However, the light transmission effect of some light transmission mirrors is still very weak after being broken. Then, this fact can show that there are other influencing factors besides the important role of residual stress. Through our analysis, experiment and calculation, it is considered that there is additional elastic stress caused by grinding, which can also arch the mirror.
Now, we can simply analyze the results of mirror grinding in an ideal state by graphic method: when the mirror blank of copper chain begins to be ground on the grinding disc, the spherical curvature of the copper mirror is basically the same as that of the grinding disc (see Figure 5), and a very regular spherical surface should have been ground, while the radius of curvature of the grinding disc and the radius of curvature of the mirror surface should be R. But in fact, when the mirror ring is tilted or the mirror surface is convex to a certain extent, the average curvature of the mirror surface becomes R (see When the mirror bounces, the decorated part is thick and hard, close to the original radius of curvature r; Where there is no pattern, it is curved, the radius of curvature is close to the value of R, the curvature of the whole mirror is inconsistent, and the divergence of reflected light is also different. As a result, a bright and dark image corresponding to the pattern on the back of the mirror appears, showing the so-called light transmission effect.
In order to prove the deformation of the mirror when grinding it, a special experiment was carried out to calculate the potential difference f between the textured and non-textured parts (see Figure 7). The results measured by laser interferometry are basically the same.
The transmission of the transmission mirror in the Western Han Dynasty depends on:
1. Its structural characteristics;
2. Under its specific structure, the role of residual stress;
3. A certain grinding technology.
These three elements complement each other to form a fully convex mirror with slightly different curvatures. Under the irradiation of sunlight, the reflected light with different curvatures is concentrated and dispersed in different degrees, and its bright and dark image is the decorative pattern on the back of the mirror, thus causing the so-called light transmission phenomenon.
Mao Zengdian teaches in the Department of Engineering Mechanics of Shanghai Jiaotong University.