Chirality & Mirrors

From WikidChem

Slides 20-25:

These slides investigated mirror images. The human mind interprets mirror images as exchanging right and left, because this is easier for our mind to handle (we've only seen people manipulate the position of their bodies, simply rotating around an axis) but in reality a mirror exchanges front and back, which is reflection across an axis. (Do you think it is clearer to say "across a plane" or "along an axis"? - JMM)

You can say either reflected across a plane or reflected along an axis. They're equivalent - just remember that the plane is the mirror and the axis is the line perpendicular to the mirror. -DTK

The statement "the mirror reverses neither right and left nor up and down," while correct, is intuitively unsatisfying. After all, it appears at first glance that the mirror does indeed reverse left and right - so why does it not appear to reverse up and down, too? The answer lies in the way we assume the person in the mirror to have turned around. We assume the person turned around the z (up and down) axis, as a person normally turns, so this axis does not appear to have been reversed. However, the person could just as well have turned around the y (right and left) axis, in which case he would again find himself facing the wrong way, but upside down instead of southpaw north. -DTK

Chirality: (from Greek word for hand) a geometric figure that cannot be perfectly overlayed on its mirror image

Using the example of a right hand, this feature can be shown by reversing the signs of each coordinate (x,y,z) one at a time. In the case of right/left hands, chirality will be shown if switching the coordinates of a right hand leads to a left hand image.

(Right hand begins in lower right back compartment)

Changing sign of all x-coordinates (reflection in yz mirror) -> left hand in lower left back

Changing sign of all y-coordinates (reflection in xz mirror) -> left hand in upper right back

Changing sign of all z-coordinates (reflection in xy mirror) -> left hand in lower right front

That changing each of the three coordinates always produces the same image (in this case, a left hand) shows that a compound can only have one mirror image, but that its mirror image can be oriented in different ways -LMM