Note it is not said one necessarily believes in an illusion, though of course one may. (See: Delusion.)

There are quite a few common illusions that are and have been widely known since Antiquity, like appearance of a straight stick when held in clear water (twisted), the appearance of the moon when it is close to the horizon (large), the appearance of things for those with jaundice (yellowish) etc . These examples also show that one may be quite certain that what one sees is an illusion, and know that it is not as it appears to one.

Illusions are interesting for psychology, because they provide data about how the human nervous system works i.e. in this case: How it gets tricked or confused by illusions.

Illusions are also interesting for philosophy, because so very much of what human beings have believed or practised was based on illusions, and because many philosophers have held that much or all of ordinary human experience is an illusion.