Right and Left 3 Mirrors

Which is which?

Material

A pair of gloves. The right and left gloves should be different and labeled.
A flat mirror
A second identical flat mirror.
A mirror bent around a cylinder.
A parabolic mirror.

Assembly

Pin a label on each glove, "right" on the right glove, "left" on the left.

To Do and Notice

Flat Mirror

Hold your right hand out toward a mirror.
Fingers toward the mirror palm down.
Look at the reflection of your hand in the mirror.
Is the reflected hand a right hand or a left hand?

Hold up the gloves one at a time, look at the glove not at its reflection!
Notice which glove would fit onto the reflected hand.

Read the label on the glove. (If you can't read the label you're looking at the reflection of the glove, don't look at the reflection.)

Notice that the reflected image of a right hand is a left hand.

Look at the reflection of the hand.
Notice that the thumb on the reflection is on the same side as the thumb on the real hand.
Notice that the palm in the reflection is down just like the palm on the real hand.
Notice that the fingers on the real hand point in to the mirror, while the fingers on the reflected image point out of the mirror.

We have changed one direction, so that the hand is turned from right to left by reflection in a mirror.

Two mirrors

Place the two mirrors so that they make a right angle.
If the mirrors were the pages of a book, the spine of the book would be straight up and down.

Hold your right hand out toward the crack between the two mirrors.
Fingers toward the mirror palm down.
Look at the reflection of your hand in the mirror.
Start with your finger tips touching the mirror then move your hand away from the mirror until it vanishes and reappears.

Hold up the gloves one at a time, look at the glove not at its reflection!
Notice which glove would fit onto the reflected hand.

Read the label on the glove. (This time you can read the label on the reflected glove, this is a clue that something is different.)

Notice that the reflected image of a right hand is a right hand.

Look at the reflection of the hand.
Notice that the thumb on the reflection is on the opposite side as the thumb on the real hand.
Notice that the palm in the reflection is down just like the palm on the real hand.
Notice that the fingers on the real hand point into the mirror, while the fingers on the reflected image point out of the mirror.

We have changed two directions, so that the hand is unchanged, a right remains a right by reflection in two mirrors.

Curved Mirror

Place the curved mirror so that its axis is vertical. That is so that the sides curve toward your right and left shoulders.

Hold your right hand out toward a mirror.
Fingers toward the mirror palm down.
Look at the reflection of your hand in the mirror.
Start with your finger tips touching the mirror then move your hand away from the mirror until it vanishes and reappears.

Hold up the gloves one at a time, look at the glove not at its reflection!
Notice which glove would fit onto the reflected hand.

Read the label on the glove. (This time you can read the label on the reflected glove, this is a clue that something is different.)

Notice that the reflected image of a right hand is a right hand.

Look at the reflection of the hand.
Notice that the thumb on the reflection is on the opposite side as the thumb on the real hand.
Notice that the palm in the reflection is down just like the palm on the real hand.
Notice that the fingers on the real hand point into the mirror, while the fingers on the reflected image point out of the mirror.

We have changed two directions, so that the hand is unchanged, a right remains a right by reflection in a mirror with one curve.

Parabolic Mirror

Hold your right hand out toward a mirror.
Fingers toward the mirror palm down.
Look at the reflection of your hand in the mirror.
Start with your finger tips touching the mirror then move your hand away from the mirror until it vanishes and reappears.

Hold up the gloves one at a time, look at the glove not at its reflection!
Notice which glove would fit onto the reflected hand.

Read the label on the glove. (If you can't read the label you're looking at the reflection of the glove, don't look at the reflection.)

Notice that the reflected image of a right hand is a left hand.

Look at the reflection of the hand.
Notice that the thumb on the reflection is on the opposite side as the thumb on the real hand.
Notice that the palm in the reflection is up the opposite of the palm on the real hand.
Notice that the fingers on the real hand point into the mirror, while the fingers on the reflected image point out of the mirror.

We have changed three directions, so that the hand is turned from right to left by reflection in a parabolic mirror.

Going Further

What does a curved mirror do when a hand is held close to the surface?
What happens when a right hand is turned so that the thumb is up and the palm faces left with the fingers toward a mirror?
What happens to a left hand?
What happens to the curved mirror if it is placed with its axis horizontal?
What happens to the reflection when a flat mirror is placed on the floor?

What's Going On?

Right and left hands are determined by 3 directions: the direction of the fingers, the thumb and the palm.

If you reverse the direction of one of these and keep the others the same you turn a right hand into a left and vice-versa.

If you reverse two directions a hand does not change.

If you reverse three of these directions you change a right hand into a left.

Physicists, chemists and mathematicians describe nature, chemicals and patterns by saying that they are right or left handed.

The definition of handedness is based on the ideas developed in the above activity.

For example, a mathematician says that a coordinate system that has its x-axis pointing out of the fingers of your right hand, and the y-axis sticking out of the palm of your right hand will have its z axis pointing along your right thumb.(If the z-axis points the opposite way this is a left handed coordinate system.)

A left handed coordinate system has the x axis along the fingers, the y-axis out of the palm, and the z-axis along the thumb of the left hand.

The vector cross-product has the definition of a right handed coordinate system built in to it. If you have a unit vector named i (a vector of length 1.) pointing along the x-axis, and a unit vector j along the y-axis then i x j = k , a unit vector along the z-axis.

An Activity by Paul Doherty developed in collaboration with Pat Murphy.