Why does the Torah see fit to define "Beis ha'Sohar"?
Ramban (citing the Ibn Ezra): Although the word appears to be a regular Lashon ha'Kodesh word, the fact that the Torah sees fit to define it suggests that it is basically an Egyptian word, since it is the way of the Torah to define foreign words. 1
Ramban: The Torah is not defining the word (which is purely Lashon ha'Kodesh), but explaining that Potifar placed Yosef in the prison where the royal prisoners were incarcerated. 2 Or, it was the prison where those who sinned against the king were incarcerated. 3
See, for example, Esther 3:7. The Ramban rejects this explanation, however.
Ramban Which explains why the chief butler and baker were later incarcerated there, and the Torah mentions it because it raised Yosef's status (See R. Chavel's notes).
Ramban: In spite of which Potifar placed Yosef there - because he loved him.
What exactly, does the word "Sohar" mean?
Ramban #1 (citing the Radak): It means 'a round arch.' 1
Ramban #2: It refers to a pit - an underground prison, with a small opening on top into which the prisoners were lowered, and which let in a little light. 2
As in Shir ha'Shirim 7:3.
Its source is the Aramaic word 'Sihara' - the moon (which is round and which illuminates). It is like the word "Tzohar" ("Tzohar Ta'aseh la'Teivah" - 6:16), so-called there because it gave a lot of light, whereas here it is called "Sohar" because it let in only a minimal amount.
Why does the Torah insert the words, "Adonei Yosef"?
Oznayim la'Torah: Potifar incarcerated Yosef without a trial - because in Egypt, a master had the right to do so to his slave. 1
Indeed, the word 'Adon' stems from the word 'Din' - a master has the right to judge his slaves or subordinates (Yerios Shlomo). See Yalkut Shorashim (Steinberg) Erech Dalet.
Why did his master not follow up on his anger by sentencing Yosef to death, as would have been expected?
Ramban #1: He declined to have him killed because he loved him. 1
Ramban #2: There is no logical reason for it. It was Min ha'Shamayim. 2
Seforno and Moshav Zekenim (to 39:19) #1: He saw how Yosef prospered and was a Tzadik. Perhaps his wife lied. And he only incarcerated Yosef to maintain his wife's honor. 3
Targum Yonasan: Potifar's anger was only momentary. He immediately consulted with the priests, who concluded that what his wife had placed on her bed (refer to 39:14:2:1) was the white of an egg, and not semen. 4
Moshav Zekenim #2: Because it would have strengthened the rumors and shamed his wife.
Moshav Zekenim, Hadar Zekenim, Riva and Rosh (all on Bereishis 47:22, from Midrash Agadah 47:26): The priests said that if his garment was torn on the back side, it would prove that she tried to seduce him and he fled. 5
Chizkuni, citing a Midrash: Yosef was brought in front of the king. Gavriel came in the form of a man, and said that they should check their garments. If her garment was torn, this shows that he tried to rape her. If his garment was torn, it would prove that she tried to force him, [and he fled].
Ohr ha'Chayim (to 39:19), Malbim (to 39:19), from Bereishis Rabah 87:9: Potifar did not believe his wife. 6
Oznayim la'Torah (to 39:10): It was a miracle, as was the fact that he left prison in order to rule - in keeping with the Gemara in Kidushin 40a, 'Anyone who is tempted with Arayos, and overcomes the Yetzer ha'Ra, merits a miracle.'
And it was to reward them for saving his life that Yosef exempted them from giving their land to Pharaoh (see 47:22:1:1). See also Ibn Ezra.
Which in fact was the case. Hadar Zekenim, citing a Midrash - Gavri'el reversed it so it was torn on the back. Riva - This is like the opinion that Yosef came to be with her, but saw his father's image and retracted. (Why was it torn in front? Was Yosef in such a rush that he could not wait to remove it? - PF) Also see 39:20:3:7.
Bereishis Rabah: He incarcerated him only lest people question the legitimacy of his children (Matenos Kehunah - from before he became castrated. If he asserted that she tried to seduce Yosef, people will say that in the past she seduced and was Mezanah with others!)
Why did Potifar incarcerate Yosef in the prison that was reserved for the king's prisoners?
Seforno: Refer to 39:19:2:1**.
Ha'amek Davar: Because Potifar was the head executioner, and this prison was under his jurisdiction.
Why does the Torah insert the (otherwise superfluous phrase), "And he was there in the prison"?
Oznayim la'Torah: To teach us that Yosef did not give up, but continued to serve Hashem faithfully in his new location just as he had done at home and when he worked in the house of Potifar. 1
Malbim: He was not incarcerated there. 2 Potifar appointed him to work there. The prison was of Potifar, and he needed people to work there.
Ha'amek Davar: To teach us that he was incarcerated on a permanent basis, to serve in whatever capacity was placed upon him, and to be fed on minimal rations - as opposed to prisoners who are incarcerated for a short period awaiting trial, who do not work, and who are fed from the royal storehouse.
