What is the precise definition of Maris Ayin, and to what cases does it apply? (i.e. what are the parameters for applying it)
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Maris Ayin (literally "the vision of the eye") describes rabbinic enactments that were put into place to prevent a third-party viewing one's actions from arriving at the incorrect conclusion that a forbidden action is permitted.
It has many applications across halacha, including the laws of Shabbat, Avodah Zarah and Kashrut.
An important additional principle is that כל מקום שאסרו חכמים מפני מראית העין - אפילו בחדרי חדרים אסור - Anything that the sages prohibited because of maris ayin is forbidden, even when it is performed in a private room (Beizah 9a). In other words, once something is prohibited by chazal for this reason, one is not allowed to rationalize that one can perform the action in private because no one will see it. (This principle is also the subject of much debate among halachic authorities).
There is no such thing as Marit Ayin, as I have stated elsewhere.