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.
IF SO:
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Can this 30' mirror extender impact anyone other than a medusa? If so, this is an effective, weaponized, range doubler?
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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.
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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'.
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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.
Best Answer
This doesn't work. The range is not extended
You can have physics or strict rules as written, not both. Trying to selectively combine elements of both gets you nonsense like the peasant railgun.
The rules say that a creature must be within 30 feet of the medusa and able to see her eyes to be affected. The rules add that the medusa is also affected by seeing her reflection on a surface within 30 feet of her. (Note that the medusa is always within 30 feet of herself.)
You are reading the rules as if they say that any creature is affected by seeing the medusa's reflection on a surface within 30 feet of themselves and the medusa. The rules don't say this. It is specifically the medusa who is affected by this.
There are several ways to interpret this. One way is that the range of the effect is measured by physical distance from the medusa, not the distance light travels between the medusa's eyes and your own, and a mirror more than 30 feet from the medusa has the eyes too small to see clearly. Another way is that the gods were cruel and cursed the medusa to be even more vulnerable to her own gaze than other creatures. After all, the clause you focus on is "due to its curse".
She could use mirrors to Gaze around corners, though
The rules specify seeing her eyes and being within 30 feet of her. With an appropriate set-up, she could use mirrors to be visible to creatures around a corner but still within 30 feet of the medusa. Effects which can go around/through obstacles but have the range measured in travel path rather than straight lines usually say so, but the medusa's Gaze does not, so one could reasonably rule to measure in a straight line.
Of course, why would a medusa want to put mirrors in her own lair? That is of more danger to herself than any potential interlopers. A tactically minded medusa would instead ensure her lair does not have any unobstructed straight lines longer than 30 feet, such that any ranged attackers must get within 30 feet of the medusa to attack her. (Although, this also makes it possible for a clever attacker to surprise the medusa with a mirror hiding around a corridor. Counter by not having bright light. Offense vs defense, I suppose.)
Consider creating a variant medusa with Lair Actions
Of course, this only applies to the monster's stat block as written. As GM, you are free to create your own monsters. Conceptually, the idea of a medusa who has rigged her lair to project images of herself at greater range than normal sounds neat, and fits with the mechanics of Lair Actions. (I'd use magic rather than mirrors for safety, though.) Just acknowledge that this would be a homebrewed variation on the medusa rather than the rules-as-written medusa.