Ye Magick Mirrour of Old Japan

by Silvanus P. Thompson

Plate IV. is a rather smaller mirror, 6⅞ inches in diameter, having low-relief ornament only; yet of this almost every detail is visible in the image as cast by electric light or sunlight.

Plate V. shows a mirror which has two Chinese characters in high relief, polished, with a background made up of symbols of longevity—pine-tree, two storks, and a hairy-tailed tortoise. But though these are in almost as high relief as the polished letters, only the former are to be distinguished in the image. Here again the author conceives that the two letters have been polished down subsequently to the face; the pattern of these parts having been thus, to a minute degree, forced into the reflecting surface.

Plate VI. depicts a rectangular mirror, 15 inches high by 10½ inches wide, and weighing 5½ lbs. It is the only one of this form that he has seen or heard of; though smaller square mirrors of 3 to 4 inches in the side are not infrequent. One of the latter, in his possession, an old mirror covered at the back with Chinese characters, has no magic qualities at all. The large rectangular mirror is slightly convex, but more so in its longer direction than in its breadth. The bamboos in the pattern, though not very highly raised, are in very sharp relief, the mirror being, apparently, an ichi mai buki, or artist’s proof. There are two raised lumps on the back, apparently the remains of the parts where the metal was poured into the mould; and, curiously enough, neither these nor the rims of the rocks in the foreground yield any image, though they are more highly raised than any part of the bamboos.

Plate V.

To complete the proofs that the effects are due to differences of curvature the author has made the following observations.

By holding a magic mirror very obliquely to the light one can discern traces of the pattern in the face, especially if one is accustomed to examine optical surfaces for small inequalities of curvature. For example, on examining (at oblique reflection) in such a mirror the image of a horizontal window-bar or of the roof-line of a house, one sees the straight line slightly curved downwards out of the level wherever the image is made from a slightly concave (or less convex) part of the surface. Acting on this hint the author found that if one chooses as an object to be viewed in a mirror a pattern of narrow parallel straight lines, such as a finely-striped blind, the pattern on the back of the mirror can be dimly seen in the face, resembling that species of line-engraving, sometimes used for medallion portraits, in which the whole picture is crossed by lines from side to side, the lines being bent toward one another or widened out to give effects of light and shade. Another variety of the same experiment is to place a ruled diffraction-grating of 100 lines to the inch (ruled in a silvered surface on glass) close to a bright light, and with a short-focus lens project the lines upon a screen. Then interpose the magic mirror to throw the luminous lines upon another screen, when they will be seen with the usual magic image; the bright lines concentrating into the bright parts and avoiding the darker parts of the luminous pattern.

By the use of the spherometer to measure the surface curvatures of the mirror faces, it is easy to show that the surface of the magic mirrors is actually less convex, or even slightly concave, over those parts where the substance of the mirror is thick, as compared with those parts where the mirror is thin. For example, the curvature of the rectangular mirror, Plate VI., as measured from left to right over the convex surface, is, on the average, about 0·2 dioptries (or its radius of curvature is about 5 metres), but when measured at points over the vertical bamboo stems, its curvature falls to less than 0·05 dioptrie, and in some parts is absolutely flat, or even slightly concave.

Makers of mirrors and lenses for large telescopes are accustomed to test the perfection of their figure by a process known as Foucault’s, in which the observer, after allowing light to fall from a single well-defined point upon the (concave) mirror at nearly normal incidence, places his eye at the point where the reflected rays converge to a focus, and then sees the whole surface of the mirror uniformly bright, save only such spots as differ in curvature from the rest. In the case of convex mirrors it is needful to interpose a large auxiliary convex lens to reconcentrate the otherwise divergent beam. Applying this method of investigation, the author finds that it is quite easy in many cases to see in the front face the pattern that the mirror bears on its back.

Lastly, the author has made one absolutely direct proof of the inequalities of curvature of the front surface. He took the mirror depicted in Plate I., and having taken a mould of its face in a composition of gutta-percha, he deposited a firm layer of copper in the mould by the electrotyping process. The type so made was silvered and polished, when it was found to reflect from its face the image of the bird that was on the back of the original mirror; the image was, however, less regular than that from the mirror’s own face. Here, then, was a magic mirror without any pattern on its back.