ÐÓ°ÉÔ­´´

Q: Why is an image in a mirror inverted left to right but not top to
bottom?

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A: The mirror does not reverse images from left to right, it reverses
them from front to back relative to the front of the mirror. Stand facing
a mirror. Point to one side. You and your mirror image are pointing in
the same direction. Point to the front. Your mirror image is pointing in
the opposite direction to you. Point upwards. You both point in the same
direction. Now stand sideways on to the mirror and repeat. You are now
pointing in opposite directions when you point sideways. Place the mirror
on the floor and stand on it. This time you point in opposite directions
when you point upwards and your upside down image points downwards. In all
cases the direction reverses only when you point towards or away from the
mirror.

Hilary Johnson Malvern, Worcestershire

* * *

A: The answer stems from the fact that a reflection is not the same
as a rotation. Our bodies have a strong left-right symmetry, and we try
to interpret the reflection as a rotation about a central vertical axis.
We imagine the world in front of the mirror has been rotated through 180
degree about the mirror’s vertical axis, and it has arrived behind the mirror
where we see the image. Such a rotation would put the head and feet where
we expect them, but leave the left and right sides of the body on opposite
sides to where they appear in the reflection.

But if instead we imagine the world to have been rotated about a horizontal
axis running across the mirror, this would leave you standing on your head,
but would keep the left and right sides of your body in the expected positions.
The image would then appear top/bottom inverted, but not left-right.

So whether you see the image as left-right inverted or top-bottom inverted
– or for that matter inverted about any other axis – depends upon which
axis you unconsciously (and erroneously) imagine the world has been rotated
about.

If you lie on the floor in front of a mirror you can observe both effects
at once. The room appears left-right reflected about its vertical axis,
while you interpret your body as being left-right reflected about a horizontal
axis running from head to foot.

Peter Russell London

* * *

A: Actually, a mirror does not invert at all. Look at your face in a
mirror: the left side appears on the left and the right on the right.

Now look at someone else’s face without a mirror. It has been inverted
because of the rotation necessary to turn and look at you: their right side
is on your left. They could equally well turn to look at you by standing
on their head, in which case you see their left on your left, but now
the top of their head appears at the bottom. We don’t normally do this
because it’s not very comfortable.

Try this experiment. Write a word on a piece of paper and hold it up
to a mirror. You automatically rotate it about a vertical axis and it appears
in the mirror inverted left to right. It is this rotation which inverts
the image, not the mirror.

Try the experiment again, and this time when you hold the paper up to
the mirror, rotate it about a horizontal axis. The word will be inverted
top to bottom.

Alan Harding Stansted, Essex

* * *

A: The problem is caused by the way we visualise the mirror image. We
imagine ourselves standing on a carousel, which has done a half turn to
put us where we see the image – that is, in the mirror. We see that the
top and bottom of our bodies in the mirror image are in the same place,
but left and right are reversed.

If instead of a carousel we used a ferris wheel to rotate ourselves,
and imagined ourselves strapped upright in the seat we would see a different
result. When the wheel does a half turn, the mirror image now has left
and right in the correct places, but top and bottom are reversed.

The trouble is that we are incorrectly using rotation for these experiments,
when, in reality, the mirror reflects front-to-back. Because this is a
difficult thing to do with our body, we mentally substitute rotation, which
doesn’t quite fit what we see.

Generally, we prefer to keep top and bottom correct, so we see a left
to right reversal in a mirror, although we could see top to bottom reversal
if we wished.

David Singer San Francisco, California

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This question has provoked a greater number of replies than any other.
More than 150 were received and this is just a small, but representative,
selection. The decision over which answers to print was a very difficult
one but New ÐÓ°ÉÔ­´´ would like to thank everybody who took the time to
respond.

Shiny, happy hair

Q: Why, if hair is dead, does my physical or emotional state affect
its condition? When I am ill, my hair is dull and lifeless. Conversely,
when I was pregnant, my hair was lustrous and shiny.

* * *

A: Hair is indeed dead. However, its appearance and condition depends
upon secretions from the sebaceous gland at the hair’s base. Too little
secretion, and the hair becomes dry, brittle and liable to damage; too
much, and it is greasy and lifeless.

Clearly, these secretions are likely to be affected by the hormones
(as in pregnancy), or by serious illness.

With minor illness and emotional upsets, it is more likely that a change
in hair care routine is to blame – perhaps along with heightened sen-sitivity
to imperfections in one’s appearance.

Alison Brooks Rugby, Warwickshire

This week’s questions – Star turn

Star turn: How many stars have astronomers located in the Universe,
and how many of them have been named? Is there any body that supervises
or records the naming of stars and any regulations that apply to their naming?

M. J. Jolliffe Bertrange, Luxembourg

This week’s questions – Mad tidings

Mad tidings: Can anyone explain in simple and common-sense terms why
there is simultaneously a high tide on both sides of the Earth?

Pat Sheil Sydney, Australia

This week’s questions – Milky milky

Milky, milky: Every day I buy a pint of full-cream milk and one of semi-skimmed
milk. I would expect the full-cream milk to go off first but, other things
such as refrigeration being equal, it is the semi-skimmed that most quickly
becomes undrinkable. Why?

Fred Pearce London

Scaling trees

Scaling trees: The resident green snakes in Malaysia are up to 90 centimetres
long and can climb coconut trees. The snakes cannot encircle the tree trunk
but I understand that they can get a purchase on the bark of the trunk
when climbing upwards. This is because their scales, facing back from their
heads, will tend to move away from the body and dig into the bark slightly
as gravity acts against the snake. But what holds them to the trunk when
they turn to descend? How do they get down without falling?

Richard Forbes Donald-Hill Kuantan, Malaysia