"Medusa's gaze" is a figurative expression used to refer to a particular type of facial expression. However, it has nothing to do with translucent creatures that live in warm seas and oceans.
The expression "The Gaze of Medusa" is based on the ancient Greek legend of the Gorgon sisters.
Medusa Gorgon
According to legend, a gorgon named Medusa was one of the three sisters, a woman who had a ball of wiggling snakes instead of hair. It is believed that it was the noticeable similarity between the head of a jellyfish with wiggling snake hair and the tentacles of a sea or ocean jellyfish, which also constantly wriggle, that gave rise to the name of this marine life.
However, her danger to travelers who appeared near her habitat was not so much in her terrible appearance, which frightened them, but in the action of her gaze. According to legend, who saw the eyes of the gorgon Medusa turned into a stone statue. This ability of hers allowed her to gain numerous victories over her opponents, turning them to stone. The only one who was able to defeat her was the hero of ancient Greek myths named Perseus, who was warned in advance about her such ability. Therefore, going to battle with the gorgon Medusa, he armed himself with a shield, which was given to him by the goddess Athena.
This shield had a very smooth polished surface, in which Perseus saw all reflected objects as clearly as with his own eyes. This also applied to the image of the gorgon Medusa, but her reflection no longer possessed the magical power that her gaze had, so Perseus was able to avoid the fate of being turned into stone and cut off Medusa's head.
At the same time, the severed head of the gorgon retained its magical abilities, which Perseus himself could later use, performing his feats of arms. So, using the head of Medusa, he turned the sea dragon Keto, king Polydect and his other opponents into stone.
The Gaze of Medusa
Today, the expression "The Gaze of Medusa" is used within the context of this legend, referring to the events that took place during the battle between her and Perseus. Of course, it should not be taken literally, since no one person has the ability to turn another person into stone with the help of a glance: it is used mainly in a metaphorical sense. So, the use of this expression in relation to a person means that his gaze seems to those around him heavy, disapproving or even hating.
Usually, such an expression is rarely used in communication with such a person himself, but it can be used by others to describe it to other people.
