This interesting report on a Korean study in the American Journal of Ophthalmology reports that sleeping on one side may worsen glaucoma on that side.   Some quotes:

People with worsening glaucoma on just one side were also more likely to sleep with the affected eye facing downward. The researchers say that position raises the eye's internal pressure and probably hastens deterioration of the eye.

Certainly, if one has severe damage in one eye it would seem to make sense to attempt to...sleep on the side with less eye damage - or on your back. But Schultz warns that sleeping on your back may not be the answer for people who are predisposed to sleep apnea, which is another risk factor for worsening glaucoma.

SOURCE: American Journal of Opthalmology, online December 15, 2013.