When or even if, the exodus occurred is often a topic of debate and much conjecture. Admittedly, it's tricky. However, what makes things unnecessarily difficult is the academic establishment's disdain for the Bible, specifically, and traditional sources in general. They've sought to create an ancient timeline independent of, and very nearly antagonistic to, the Bible. There are many reasons why this is a really bad idea. A really big one, is that before the 19th century, the Bible was the only source of information we really had about the ancient world. It is the most complete and comprehensive source of information about the ancient world. What we've obtained since hasn't been nearly as comprehensive. We have much passed down by the Greeks, but it isn't nearly as ancient as the Bible. Abraham, after all, came from one of the oldest known cities, Ur, in Mesopotamia. The Bible represents an effort to restore history, and Man's relationship with the Creator, before it was corrupted by the early civilizations. Knowing the nature of civilization, past and present, that is not a hard sell. Archaeology, the big, relatively new, historical discipline is the problem. It doesn't know it's place, but that is another entry.
At any rate, As a historian, my focus is on the narrative, sources and what makes sense in the greater context of history. I am a great believer in taking traditional sources very seriously, if not always literally. If we take the Bible seriously, then the key part of the story is Joseph's Dream--the Bible never names the pharaoh he serves. During the reign of Pepy II, longest reigning pharaoh of any dynasty, there was a once in a thousand years drought event. Possibly, it was the drought of Joseph's dreams. It doesn't appear that Pharaoh Pepy's rule was interrupted by it. The dynasty ended with his reign because he lived so long that even his heirs were older than customary, and of necessity, he had delegated a great deal of authority. The Intermediate Period that followed was more of a temporary decentralization of power than chaotic upheaval.
If this is the time of Joseph, which seems likely, then adding 400 years would place the Israelites exodus under Moses around the time of the Hyksos rule in Amarna. The rule of the Hyksos is seen as a time of Egyptian humiliation. Some folks identify the Hebrews as the Hyksos, but I am inclined to think that Hyksos rule is likely a consequence of the exodus, not the event itself.
Also interesting, are the findings of Dr. David Rohl are intriguing and lend
credence to ideas that I've been pondering for awhile. Dr. Rohl has
believes the tomb of Joseph has been found. He also places the Hebrews
in Egypt much earlier than others do. I am inclined towards his chronology, but not necessarily his assumption that the tomb he has identified as Joseph's, is actually Joseph's. I don't think he's outright wrong, but just that it would be very hard to prove. To be continued.