How did the world become increasingly divided into east and west between 1492 and 1800?
The starting point for this time period should give you a hint as to how the world became more divided in those years. The starting point is, of course, the year in which Columbus sailed to the Americas and in which the Moors were finally expelled from Spain. Both of these were consequential.
Both events served to diminish the amount of contact between the Middle East and the West. After the Moors were expelled, there was no Muslim presence in Europe and the two societies grew apart. After Columbus "discovered" America, European trade came to focus much more on the Americas instead of focusing (as it previously had) on trade with Asia, most of which came through the Middle East.
This is an oversimplification, of course. There were ways in which the East and West came together during this time as more contact was made with China and as the British took more control over India. However, the basic idea holds. The West stopped having nearly as much contact with, especially, the Muslim world of "the East" in the years after 1492.