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)
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.