A mirror is a surface with good specular reflection that is smooth enough to form an image. The best known example is the plane mirror. The most common use is in the home for personal grooming but mirrors are also used in scientific apparatus such as telescopes and lasers, and in industrial machinery. Most of mirrors work with visible light, aiming the visual perception. However, the specular reflection of other waves also is used.
In a plane mirror, a parallel beam of light changes its direction as a whole, whilst still remaining parallel; the images formed by a plane mirror are virtual images, of the same size as the original object (see mirror image). There are also parabolic concave mirrors, where a parallel beam of light becomes a convergent beam, whose rays intersect in the focus of the mirror. Finally, there are convex mirrors, where a parallel beam becomes divergent, with the apparent intersection occurring behind the mirror. Note that spherical concave and convex mirrors do not have a single focal point, as often described in high school physics text books (see spherical aberration in lens (optics) and aberration in optical systems).
A beam of light reflects off a mirror at an angle of reflection that is equal to its angle of incidence. That is, if the beam of light is shining on a mirror's surface at a 30° angle from vertical, then it reflects from the point of incidence at a 30° angle from vertical in the opposite direction.
For an object with approximate reflection symmetry, a reflection in some mirror plane corresponds to a combination of:
a translation if the mirror is parallel to the symmetry plane of the object, and otherwise a rotation about the line of intersection of the two planes by an angle which is twice the angle between the two planes
a reflection in the approximate symmetry plane of the object (due to the assumption this is a minor change)
A street scene reflected in a mirror with bullet holes, during the siege of Sarajevo. Photo by Mikhail EvstafievWe can apply this to the image in a mirror of, say, a standing person, because people have approximate bilateral symmetry. The image is the most realistic if it is still vertical, i.e., if the rotation is about a vertical axis. This is the case if the mirror is vertical. In this case the image of the person is in normal standing orientation and vertically in a normal position, at a horizontally different position and with an orientation rotated about a vertical axis, the latter except if the mirror is parallel to the approximate symmetry plane of the person.
In particular, if one looks at one's image in a vertical mirror in left-right orientation, the image corresponds to a rotation by 180° about the vertical axis in the mirror, combined with a reflection in one's approximate symmetry plane.
The question is sometimes asked, "Why does the mirror reverse left to right and not top to bottom?", and it is worth thinking about. The counter-intuitive answer is that it actually does. Imagine you had a complete copy of your body that you could manipulate into different positions, and imagine that it is directly in front of you and facing the same direction as you, so that you are looking at its back. If you twist the copy around the vertical axis, as if it were turning to face you, and then compare that with your reflection in the mirror. The reflection will be different from the model because everything that should be on the left will be on the right.
But imagine instead that you twist the model about a horizonal axis, as if it were doing a handstand. The model would be upside down, facing you. If you compare this to yourself, and the reflection, then left and right are all correct. Your wedding ring, eye patch, and false leg are all on the correct side, be that east west north or south, but something is glaringly wrong about the reflection compared with the model, the reflection's feet are down at the bottom, where its head should be! Or, you could just keep the model in front of you so that you are looking at its back, and compare that with the reflection. Now left, right, up and down are all correct, but the reflection has its back where its front should be.
The model represents the way the 'real you' ought to look. If some other person looks at you, what would they see?. So you compare the reflection against what you think you 'ought' to see. If you think you ought to see what you look like when you're doing a handstand, then the reflection is upside down, and if you think you ought to see your own back, then the reflection is flipped front and back. But most people want to see themselves from the front, whilst standing up, they think their reflection ought to look like they would look if they turned around, and they think that left has been flipped with right.
In some sense what has 'really' been flipped is front and back. If you were to describe the body with co-ordinates, east/west north/south up/down, and the mirror has been facing south whilst you are looking north, then the difference is in the north/south direction; front and back. So I don't think my reflection looks a bit wrong because left has flipped with right, I think it looks hideously deformed because it has a face where the back of its head should be.
The mathematical or geometrical version of the question is: "why does a chiral object (such as a right hand or glove) appear as an object of opposite chirality (left hand or glove) in the mirror?" The answer is that chirality of the three-dimensional space is dictated by the choice of the directions of the three axes. When the direction of one axis is reversed, as is the case in a mirror image, the chirality (or "handedness") of space changes to the opposite one. If two mirrors are set side by side (with, say, a 90° angle between them), the axes in the doubly reflected image are inverted twice and the "handedness" of the image is not changed. In such a double mirror, a right hand looks like a right hand. This set-up lets you see how you really look, but most people find it very difficult at first to use a mirror like this for shaving.
2006-06-27 04:56:26
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answer #6
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answered by Miss LaStrange 5
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