Why "the" in "looking in the mirror"?

I rather like this question because it queries an often used idiom that I have never seen queried previously.

My simple answer is that at the moment of looking in a mirror there is only one mirror in question - the mirror that I am facing. All others are irrelevant to what is happening. Being unique, the mirror in which I look merits the definite article rather than the indefinite article.

I can't begin to think about how to research this notion, but . . .

How magical a mirror is! It's like an oracle that one consults: The Mirror. Capital T, capital M

Here's an example sentence from the OED at mirror, n. II. A reflective surface, and related senses 4. a. :

_{1766   J. FORDYCE Serm. Young Women II. viii. 88   Next morning the mirror is consulted again.
Source: Oxford English Dictionary (login required)}

Plus, this magical thing can be in any number of places at once, such are its powers! You can consult it upstairs, you can consult it downstairs, I can consult it next door.

Like the mercury once used to make mirrors, and as in a thermometer when dropped: many silvery balls but still only one mercury, always reflecting the gazer.

Consult a mirror cracked into a thousand pieces, and you'll see a thousand of yourself. The moon sees many ponds, but the ponds see only one moon.

_{Food for thought: The History of Mirror: Through A Glass, Darkly}

_{PS: I have not started drinking yet today.}

“The” has several functions in English. Some of them are:

• to reference a previously-mentioned noun: there was a dog; the dog was happy
• to specify: the middle hat
• to elevate the status of a noun: the dessert (with “the” stressed and pronounced as thee without a leading vowel sound in the next word)
• to reference a generic noun: the student isn’t greater than the teacher

Your quote sounds like the generic function of the definite article if it is set in a context like, “When looking in the mirror, you see yourself.” Although there is no specific mirror in view, using the places an emphasis on “mirror” as the focus of the sentence. Consider the following:

• When looking in the mirror, you see yourself.
• When looking in a mirror, you see the self.

There is a subtle change in emphasis that follows the noun with the definite article.

In Merriam-Webster's definition for "the", there are many senses given. "Looking in the mirror" is sense 1(l), which reads

used as a function word before the name of a commodity or any familiar appurtenance of daily life to indicate reference to the individual thing, part, or supply thought of as at hand

So the idea is that it is as if the mirror has been specified earlier in the conversation, because there is assumed to be typically at most one relevant mirror at hand in whatever situation the person is in. The standard example of this usage, before personal cell phones became universal, was "called her on the phone."