Optical isomerism regarding diastereomers
Some definitions (by IUPAC):


Diastereomer: A stereoisomer that isn't an enantiomer.
Stereoisomer: An isomer that has the same bond connectivity, but arises due to differences in the spatial arrangements of atoms.
Enantiomer: Non-superimposable mirror image.


So, diastereomers do not necessarily have to be optically active. Consider cis- and trans-1,2-difluoroethene.



They are stereoisomers (connectivity is the same, but the fluorines are on opposite sides) which are not enantiomers (they aren't mirror images of each other), which makes them diastereomers.

Neither are chiral because they are superimposable on their respective mirror images. Equivalently, the presence of the plane of symmetry (which is the plane of the molecule) makes both isomers achiral.