When Potiphar's Wife Spoke Up
וַיְהִי֩ כִשְׁמֹ֨עַ אֲדֹנָ֜יו אֶת־דִּבְרֵ֣י אִשְׁתּ֗וֹ אֲשֶׁ֨ר דִּבְּרָ֤ה אֵלָיו֙ לֵאמֹ֔ר כַּדְּבָרִ֣ים הָאֵ֔לֶּה עָ֥שָׂהּ לִ֖י עַבְדֶּ֑ךָ וַיִּ֖חַר אַפּֽוֹ׃
When his master heard the story that his wife told him, namely, “Thus and so your slave did to me,” he was furious.
ויהי כשמע אדניו וגו'. בִּשְׁעַת תַּשְׁמִישׁ אָמְרָה לוֹ כֵן, וְזֶהוּ שֶׁאָמְרָה כַּדְּבָרִים הָאֵלֶּה עָשָׂה לִי עַבְדֶּךָ, עִנְיְנֵי תַשְׁמִישׁ כָּאֵלֶּה:
ויהי כשמע אדניו AND IT CAME TO PASS WHEN HIS LORD HEARD etc. — She said this when he was alone with her, caressing her. This is what she meant by כדברים האלה “things like these did thy servant do to me” — caresses such as these.

ויחר אפו על שהתרעמה מפני שהביא לה איש עברי לצחק בה כי אמנם לא חרה אפו על יוסף בזה שהאמין יותר לדברי יוסף אבל נתנו בבית הסהר להראות שהאמין לה לכבודה ונשתמש ביוסף בבית הסהר כאמרו ויפקוד שר הטבחים את יוסף אתם:

And his angler flared: On account that
she complained of his bringing a Hebrew
man to “play” with her he did not become
angry with Joseph because he believed
Joseph’s account more. However, he put
Joseph in prison to show that he believed
here out of respect for her, but he
continued to use Joseph while in jail as
they said “And the chief servant placed
Joseph in charge of them.” (Gen. 40:4)

ואין ספק שאדוניו של יוסף למה שראה שי"י אתו לא האמין לדברי אשתו שאם היה מאמין היה ראוי שיהרגהו אבל עכ"פ הנה התפעל מזה ושמו בבית הסוהר שאם לא היה עושה זה היה לבוז בהיות אשתו אומר' כן ואם היה מחריש היה נותן לה לב לזנו' תחתיו. וז"א ויהי כשמוע אדוניו את דברי אשתו כי לא התפעל מהמעשה לפי שלא האמינו ולא ג"כ מהבגד שנמצא בידה כי אין ספק ששאל את יוסף ושהוא ספר לו האמת אלא שהתורה קצרה בזה להיותו מבואר מכח המסופר. לכן לא אמר ויחר אפו על יוסף אלא ויחר אפו בלבד כי חרה אפו במה שדברה אשתו ומה לעשות לה ואשתו אומרת כך היה הדבר ולכן חשב לשומו בבית הסוהר שהי' הסוהר מתחת ידו ובביתו לשבת שם עד יעבור זעם.
Undoubtedly, when Joseph’s master, appreciating that God was ever-present in his mind, did not believe what his wife was saying; for had he done so, he would have had to put him to death. However, he was still troubled by this episode, and accordingly put him in prison – had he not acted in this way, he would have become a laughing-stock, as his wife was (already) saying as much. By remaining silent, he would have provided her with a pretext for being unfaithful to him. This, then, is what Scripture intends to convey by the phrase, ‘And when his master heard the words of his wife’ (39:19): – for he was not unduly affected by the incident itself, since he lent it no credence; nor was he influenced by the robe found in her hand – as he undoubtedly questioned Joseph about it, and was told the truth. The Torah mentions this only briefly, as it is quite clear from the basic drift of the narrative. Hence it does not say (39:19): ‘And his fury was aroused against Joseph’, but simply, ‘his fury was aroused’. He was angered by what his wife had said, and his mind pre-occupied with what to do to appease her, given that she was insisting on her version of events. Accordingly, he resolved to incarcerate Joseph in the prison-house, which was under his control and located within the precincts of his own home, to remain there until (his wife’s) fury had subsided.

Rabbi Rachel Barenblatt (The Velveteen Rabbi):

The Hebrew for the multicolored coat is כתנת פסים (k'tonet pasim); the word in the Potiphar story is בגד (beged), "garment." A quick dip into my Brown-Driver-Briggs tells me that the three-letter root בגד means "garment, clothing, raiment, robe" when it's a noun...and "act or deal treacherously" when it's a verb. Okay, there's definitely something interesting happening here. Potiphar's wife's attempted treachery (בגד) leaves her with a robe (בגד) in her hands. And though Joseph's tunic isn't a בגד it leads to his brothers' betrayal, hinting at the synonym for clothing that the text doesn't use.

Given the resonance between the two kinds of beged, why doesn't the text use that word at the start of the story? Why is Josph's multicolored garment a k'tonet? This commentary notes that k'tonet is the name of the garment worn by the High Priest, and it's also the name of the garment God stitches for Eve and Adam out of skins. Are we meant to infer that Joseph prefigures the High Priest in some way, or to compare him with Adam? (Some commentors note that when Joseph was presented with temptation, he remembered Adam's error, and his fear of punishment kept him on the straight and narrow.)

Reb Tirzah Firestone notes here that another figure in Torah wears a k'tonet passim: Tamar, also violated by a sibling. "These Technicolor coats carried some heavy karma," Reb Tirzah writes. "In both stories, the jackets are the props spelling specialness that ends in sibling violence." She sees special resonance in Joseph's shift from k'tonet to beged: the k'tonet is "the garment of our identification, our story line. Our story might be about our greatness; it might be about how much we have suffered or the way in which we have uniquely suffered, it doesn't matter. These identities, like the k'tonet passim, keep us special and hence, keep us separate." Joseph relinquishing that garment -- and, later, relinquishing his beged in order to keep his honor -- is a sign of his transformation.