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The Semantics of Plane-Mirror Inversion

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The Semantics of Plane-Mirror Inversion NEWS AND VIEWS The semantics of plane-mirror inversion Those who ask why mirrors "invert right and left", but not "top" and "bottom", must not look for help in physics textbooks, but in dictionaries that define the use of words and in an understanding of reality. IT is, of course, a commonplace that people ment of any kind, such as would be needed stellar surface to observe the arrangement will say that an image in a plane mirror is to bring about left-right or even top-bot­ of the objects. It is as if the object in view inverted in the sense that 'right' is re­ tom inversion, but only inversion in a is flattened onto the mirror, and one is placed by 'left'. You only have to look, direction perpendicular to the plane. enabled to look at it from behind. This is and you will see! Hold up your right hand, That point is easily verified. If X is a also what happens with the image of one's palm forward, in front of a plane mirror, vector in front of and anchored into the face in a plane mirror; the mirror captures and you will see what looks like a left hand surface of the mirror, and n a unit vector a front view of one's face and also enables facing back at it. Moreover, the image is perpendicular to the mirror anchored at one to look at it from behind. The trick clearly not just a flat two-dimensional cut­ the same point, the component of X per­ amounts to nothing more than the inver­ out; if you keep the hand fixed, but move pendicular to the mirror is(X·n)n and the sion of the perpendicular components of your head, the mirror will reflect light component in the surface of the mirror is all vectors in the mirror surface. from a slightly different subsurface of simply X - (X·n)n. The effect of reflection Grand philosophical questions natu­ your hand, and so the image will seem is simply to replace n with -n, so that the rally arise, but should be dismissed. There itself to be three-dimensional. reflection of the vector X is simply is, for example, the issue of' reality', much If all this is accepted, then an uncom­ X - 2(X·n)n. All that means is that the discussed by people such as Hume and fortable question usually arises: if reflec­ image of a point a certain distance in front Kant. Is the image in a mirror real? Clearly tion in a plane mirror inverts right and left, of the mirror is displaced by twice that it is not. The most that can be said is that an why does it not also invert top and distance towards the other side of the observer can reconstruct the supposedly bottom? Often one comes across explana­ surface, and that there are no lateral real object that generates the image once tions based on the assertion that the displacements. the rules are known - that the left seems horizontal plane is distinguished from the How, then, does the illusion of left­ to appear on the right, for example. vertical in that human beings have two right displacement arise? Horsfield goes But even that does not put an end to eyes which, between them, define a unique on to argue that, whatever the mechanism, philisophical objections. Who, after all, horizontal plane, but that there is no means the illusion is incomplete. A person with can know what exactly happens within by which a unique vertical plane is defined hair parted on the left who looks into a our heads in the direct perception by the by the physiology of the onlooker. There mirror will see an image of what appears eyes of objects placed in front of them? are all kinds of philosophical objections to to be a person with hair parted on the left­ However perception works, may it not be arguments of that kind, but the most tell­ hand side. But if the image is to be taken as likened to a system of mirrors that leads, ing way of turning them is the simple that of the face of a real person, the parting willy-nilly, to the formation of an image observation that even a one-eyed man will of the hair will be on that person's right. by means that are in principle no different see the reflection of his right hand in a So the image does not correspond exactly from the formation of an 'inverted' image plane mirror as what seems to be a left to the appearence of the person in front of in a plane mirror? And while all the mem­ hand. Another is to suppose that the ob­ the mirror. And the lateral inversion oc­ bers of a group standing round, say, a table server reclines horizontally in front of a curs only in "the observer's mind". will be tempted to vote for the proposition plane mirror; again there is no inversion of Horsfield attributes the root of the that "That is a table", there is no objective top and bottom, but again a right hand is trouble to people's common determina­ way of demonstrating that all of them are reflected in an image looking like a left tion to personify the images they see as seeing the same thing. hand. reflections in mirrors. By way of antidote, Historically, arguments like these So what is the explanation? E. C. it could be worthwhile for all of us to prompted Ernst Mach's positivist view of Horsfield from the University of Durban compare our reflections in a mirror with a reality - that the only attributes of a has now persuaded the European Journal photograph taken by a camera, when the physical object with significance are its of Physics to let him publish a solemn two images would again suffer left-right measurable attributes. But even that is discussion of the issue (12, 207; 1991) inversion. But the only long-term remedy only half the battle. Have not generations which appropriately begins with quota­ is to believe the truth- that all images are of young people been drilled at school to tions from well-known undergraduate texts virtual images, without reality, just as are measure the 'position' of a mirror image asserting that "images in a plane mirror the virtual images supposed in the el­ by sticking pins in an optical bench, look­ have right and left interchanged". They ementary optics textbooks to be formed in ing for the position at which the image are all, of course, "fallacious". front of (not behind) convex spherical appears not to move? The truth is that Horsfield's view is that the underlying mirrors. these experiments do not measure an at­ error in these statements is that their au­ Astronomers and those who read their tribute of the image, but rather identify a thors confuse "physics and psychology" journals are well used to the difficulty: fixed point from which all rays reflected in - the reflection of light in mirrors and photographs of the sky habitually have a mirror from a common origin appear to what observers construe of the images 'East' on the left and 'West' on the right, diverge. The trouble is simply semantic­ they see. And, correctly, he points out that yet nobody seems to tum a hair. The ver­ that of pretending that the image is an the only possible effect of a plane mirror bal explanation is simple. The mirror im­ object. The remedy is not the obvious that may be taken as inversion of any kind age of the sky is simply the projection onto abolition of 'image', for the word is alto­ is that in which an array of points on a a mirror of what seems to be a surface full gether too useful for that. The best course straight line perpendicular to the surface of steller objects. One's view of the image is simply to remember that all images are of the mirror will appear, in reflection, to is then what one would obtain if it were unreal. be inverted. There is no lateral displace- possible to position oneself behind the John Maddox NATURE · VOL 353 · 31 OCTOBER 1991 791 © 1991 Nature Publishing Group.
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