The 5e Medusa has a 30' Petrifying Gaze ability:
When a creature that can see the medusa's eyes starts its turn within 30 ft. of the medusa, the medusa can force it to make a DC 14 Constitution saving throw if the medusa isn't Incapacitated and can see the creature.
A Medusa's Petrifying Gaze also reflects, as follows:
If the medusa sees itself reflected on a polished surface within 30 ft. of it and in an area of bright light, the medusa is, due to its curse, affected by its own gaze.
To be petrified by her own gaze (reflected back) by a mirror / shiny surface exactly 30' away must mean her petrification-curse-ability's range has been effectively doubled (60'). Thus, this self-attack rule means any mirror &/or polished surface can effectively double a medusa gaze-strike range or distance.
Let us assume that any mirror-reflection-surface (including water - or - polished shields from gods) double-extends this effective gaze-curse-range.
Can this 30' mirror extender impact anyone other than a medusa? If so, this is an effective, weaponized, range doubler?
Can this 30' range be extended via yet another mirror? If so, a chain of mirror-like surfaces could extend the curse-range ad infinitum.
Can any mirror contribute to this extension-conspiracy? If so, any clever medusa could make a mirrored &/or reflective hallway (up to 30' wide) of any length and launch her gaze-curse weapon-attack down this tube-tunnel (both safely & effectively), impacting anyone on the far end. She could also make the floor and ceiling 'polished surfaces' so as to guarantee this gaze-attack is not inadvertently lost should it bounce non-reflectively 'up' or 'down'.
How about mirrors in & around corners &/or bends: Having mirrors placed strategically about a mirrory-maze allows her to strike archers and line-of-sight attackers with great efficiency and impunity. Note: this is a great time to use the word 'impunity'.
There are many more questions, of course, you already get the gist. Typically in D&D 'line of sight' is not bendable nor extendable. If this 'general' rule is over-ruled by the 'specific', my NPC Medusa is prepared to have a lot of fun. In fact, she may even call up Poseidon and Athena for a little payback.
Repeat Of Question:
Can a Medusa (5e 'monster') have her gaze's range extended and effectively doubled via a mirror?
If so, what are the limits on such extension?
This question is related to this question - they explain this as The gaze is NOT like a line-of-sight weapon - instead this gaze-effect is more like a qualified aura-effect. This gaze could bounce off of the moon and back - only those within 30' of the girl are impacted. As this Medusa is (obviously) within 30' of herself, she is impacted regardless of how much distance her gaze has undergone.
Another example: To see a Medusa's face a mere inches away via scrying is only dangerous if you happen to be physically within 30' of her. One Levitating 31' above a Medusa whilst using the best binoculars is safe as long as she cannot jump more than eleven inches.
Conversely, if there is a mirror that reflects her image through a Gate, anyone that sees this image while within 30' of her (including the Medusa herself) must make a saving throw.
Weirdly, Darkvision, Demonsight, web-sense, echolocation and any other vision that works in total darkness is also perfectly safe - until she lights a match ('dim light or better')
It is a very weird curse. I am glad I asked, thank you.