Reflections on The Mirror Question
When looking in your rear-view mirror, objects in front of the mirror
(as seen in the image in the mirror) are reversed left and right, but
not up and down. Why are left and right reversed, but up and down
are not? To answer this commonly-asked question, we need to first
answer the question: "Reversed relative to what?" From the context
of the original question we can infer that it refers to the image in
the rear-view mirror being reversed relative to the image we would
see if we turned around and looked directly out the back window. If
so, then the answer depends on HOW we would turn around. Most likely
we would rotate our field of view about a vertical axis, so the image
we see will be reversed laterally (left-to-right). Of course, if we
turn about a horizontal axis (difficult to do in a car, but not
impossible), the image we see would be reversed top-to-bottom.
Another answer that is often given to this question is that mirrors
reverse neither left-to-right nor top-to-bottom, they reverse front-
to-back. This is actually the answer to a slightly different question
than the one asked above, but it's such a cute answer that many people
can't resist giving it whenever anyone asks anything about mirror
images.
The reason there are consistently conflicting answers to "the mirror
question" is partly due to the fact that the question is often poorly
expressed, so that it can be construed in several different ways.
The ambiguity is two-fold, because, first, the question often doesn't
explicitly identify the two things that are posited to be "reversals"
of each other, and second, the question often doesn't define the
intended sense of "left" and "right", i.e., as relative directions
or as designations of "handedness".
Thus, if someone asks "Why do mirrors reverse left-right?" we could
imagine that he's asking
(0) Why, as I look at a mirror, do objects that are actually on
my left appear to be on my right, and vice versa?
In other words, he's assuming a fixed set of relative spatial directions
based on his current orientation as he looks at the mirror, and he's
asking how the directions of the actual objects compare with the
directions of their reflected images. Of course, on this basis we're
forced to conclude that the PREMISE of the question is totally erroneous,
because it's obvious that objects to the left of the viewer appear to
the his left in the mirror. Thus, if we assume this interpretation we
have the fun of telling him that he's so stupid, even the PREMISE of
his question is wrong, i.e., he's asking for an explanation of why
something occurs when in fact no such thing occurs! Hah! It's always
deeply satisfying when we can slam someone like this, thereby
demonstrating the clear superiority of our thought processes.
for more go to
http://www.mathpages.com/home/kmath441.htm
silly Calgon. Hugs, Mariposa