Material

A manila folder.
A Pen
Scissors
A flat mirror
A second and third identical flat mirror.
A mirror bent around a cylinder.
A parabolic mirror.
A Red stick-on dot and a green dot.

Assembly

Put a hand face down on the manila folder and use the pen to trace the shape of your hand.

Cut the hand shape out of the manila folder.

To Do and Notice

Prolog

Show people the hand cutout and Say "This is a trick question.
Is this a right hand or a left hand?"

It's a trick because the cutout is neither a right hand or a left hand until you indicate which side is the palm side. Draw some lines on the palm side to turn it into a right hand.

Now you have a paper right hand.

Face the mirror. Place a red dot on the side nearest your left shoulder and a green dot on the side nearest your right shoulder.

Flat Mirror

Hold your paper right hand with its palm toward a mirror and the fingers pointing up.
Look at the image of the hand reflected in the mirror.
Is the reflected hand a right hand or a left hand?

Hold up your hands one at a time to see which matches the reflected hand. Notice that the fingers point up, which side the thumb is on (red or green) and which way the palm is facing.

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 fingers in the reflection point up just like the fingers on the real hand.
Notice that the palm on the real hand faces the mirror, while the palm on the reflected image faces 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.
Palm toward the mirror fingers up.
Look at the reflection of your hand in the mirror.

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 fingers in the reflection point up just like the fingers on the real hand.
Notice that the palm on the real hand faces the mirror, while the palm on the reflected image faces 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.

Three mirrors

Place a third mirror underneath the two above mirrors. The mirrors form one corner of a cube.

Hold your right hand out toward the vertex where the three mirrors come together.
Palm toward the mirror fingers up.
Look at the reflection of your hand in the mirror.

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 fingers in the reflection point down opposite the fingers on the real hand.
Notice that the palm on the real hand faces the mirror, while the palm on the reflected image faces out of the mirror.

We have changed three directions, so that the hand is reversed, a right turns into a left by reflection in three mirrors.

Curved Mirror

Place the curved mirror so that the sides curve toward your right and left shoulders.

Hold your right hand out toward a mirror.
Palm toward the mirror fingers up.
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.

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 fingers in the reflection point up just like the fingers on the real hand.
Notice that the palm on the real hand faces the mirror, while the palm on the reflected image faces 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.
Palm toward the mirror fingers up.
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.

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 fingers in the reflection point down, opposite the upward pointing fingers on the real hand.
Notice that the palm on the real hand faces the mirror, while the palm on the reflected image faces 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 curve toward your head and feet?
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.

Math Root

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.

Return to Draft Activities

Scientific Explorations with Paul Doherty

© 2002

19 July 2002