This Demonstration shows that if a molecule possesses a symmetry plane, the molecule cannot be chiral and its mirror image is indistinguishable. 
We consider four different molecules:
In each case, a plane passing through the molecule is shown. When no mirror symmetry exists, such a molecule is called an enantiomer. In most cases, enantiomers depend on the presence of atoms with different substituents (e.g. halothane, 1-iodo-1-fluoroethane), but chirality can occur without a chiral center as well (e.g. 1-chloro-2-fluoro-1-iodopropadiene).
Enantiomers in solution can be identified by the differing rotation of the polarization (
) of transmitted light. Enantiomers are classified as R or S chiral centers according to Cahn–Ingold–Prelog priority rules. It is worth noting that R or S does not determine the rotation angle (
We color in black carbon atoms that are not chiral centers in red and blue to mark those carbons that are chiral centers.
As there are many examples with a carbon-carbon single bond, we note that the isomerism of staggered and eclipsed conformations produces no optical activity since these forms interconvert rapidly at room temperature due to the low activation energy. 
Use the "reflected molecule rotation" slider to rotate the mirror image of the molecule to check if it is superposable with the original molecule. In enantiomers this is not possible, unless a pair of substituents is exchanged.
Allene molecules are characterized by adjacent double bonds. When the number of double bonds is odd, the molecule lies in a single plane and geometric isomerism is observed. With an odd number of double bonds, as in the example shown, the substituents can be arranged on perpendicular planes and optical isomerism is observed.