Before you read this, I suggest you read post 20.27.
The picture above shows a molecule of tartaric acid. This molecule is chiral – it is not identical to its mirror image (post 20.27). The form of tartaric acid shown in the picture is called D tartaric acid; its mirror image is called L tartaric acid (post 20.27). Since D tartaric acid is laevorotatory we could also call it D(-) tartaric acid; L tartaric acid rotates the plane of plane polarised light in the opposite direction and so could be called L(+) tartaric acid. Further explanation of the previous sentence is given in post 20.29. D and L tartaric acid are mirror images of each other.
Now let’s look at the two carbon atoms in D tartaric acid indicated by the blue and green arrows. Each has bonds pointing to the four corners of a tetrahedron (post 16.30). Let’s now think what would happen if we changed the arrangement of atoms around one carbon atom (green arrow) to the arrangement in L tartaric acid, leaving the arrangement around the other (blue arrow) unchanged.
What happens when we form the mirror image of this hybrid form of tartaric acid? The D half of the molecule becomes the L half and the L half becomes the D half. So this hybrid form is identical to its mirror image; both are half D form and half L form. The hybrid of D and L forms is called a diastereoisomer and, in this example, is written as DL tartaric acid.
Is DL tartaric acid optically active (post 20.29)? No. The reason is that one half of the molecule rotates the plane of plane polarised light to the right (the L half) and the other half rotates it to the left (the D half). So, overall, there is no rotation of the plane of plane polarised light.
We have seen that simple chiral molecules exist as D and L optical isomers. But, for more complicated chiral molecules there may be an achiral (post 20.27) form that is a diastereoisomer. It is easy to distinguish the different forms; the achiral molecule is not optically active (post 20.29). But the D and L forms are optically active – one is laevorotatory and the other is dextrorotatory (post 20.29).