Berakhot 083

40:
With regards to the Minĥah Amidah, too, there is a maĥloket [difference of opinion] between Tanna Kamma and Rabbi Yehudah. It would seem that there were basically two different ideologies current in Talmudic times as regards the time of day appropriate for Minĥah. On the one hand, we have a view – probably reflecting general opinion in Eretz-Israel – that Shaĥarit and Minĥah should be recited (ideally) im dimdumei ĥammah ["when the sun is reddish"]. This phrase means that the ideal time for Shaĥarit is at sunrise and that the ideal time for Minĥah is just before sunset, times when the sun seems bigger and redder than otherwise. In the Gemara we find this opinion attributed to Rabbi Yoĥanan, one of the greatest and most influential Amoraim of Eretz-Israel [Berakhot 29b]. Similar sentiments can be perceived in the wish of Rabbi Yosé ben-Ĥanina: "May it always be my lot to pray when the sun is reddish … at a time when the day is gradually becoming extinguished" [Talmud of Eretz-Israel, Berakhot 7b]. This view is reflected in our mishnah in the opinion of Tanna Kamma.

41:
Rabbi Yehudah's view in our mishnah reflects the second ideological stance: that the great virtue of Minĥah is that it is the only one of the three daily Amidot for which a person has to deliberately interrupt their daily schedule, take a break from mundane business, and spend ten minutes or so in communion with the Deity [see Tur Oraĥ Ĥayyim 232:1]. It is possible that this view – later much admired by mystics – reflects the general opinion of Babylonian Jewry.

42:
Tanna Kamma sets the 'deadline' for Minĥah at sunset. Rabbi Yehudah sets the 'deadline' for Minĥah about an hour and a quarter before sunset, at a point in time called plag ha-Minĥah. I bring here an extensive quote from Berakhot 005:

43:
It remains for us now only to explain the term plag ha-Minĥah. We have already seen [Berakhot 081] that the usual time for the second of the two daily Sacrifices in the Bet Mikdash was half an hour after the ninth hour of the day. This time is referred to for the sake of convenience as Minĥah Ketanah [the Little Minĥah], since there rest only two and one half hours until sunset. But we also mentioned that on 14th Nisan in the Bet Mikdash this sacrifice was advanced to half an hour after noon. This time is referred to as Minĥah Gedolah [the Great Minĥah], since there are still five and one half hours to go until sunset. The Aramaic word Plag (as in plag ha-Minĥah) means "half". Rabbi Yehudah therefore, sets the ideal time for reciting Minĥah as being "halfway" between Minĥah Ketanah and sunset.

44:
Let us sum up the situation as regards Minĥah. It may be recited from half and hour after noon onwards. There are those who, for ideological reasons, delay reciting Minĥah until half an hour after the ninth hour of the day. It must be recited by sunset at the latest. Those who wish to recite Arvit earlier than dark must be careful to recite Minĥah by "plag ha-Minĥah". (This does not apply to Minĥah and Arvit on Erev Shabbat.)