Last Sunday, our lesson was from Ex. 32-34. As I prepared to teach, two questions came to mind. First, I have noticed the #40 occurs often in the bible. Moses was 40 years old when he killed the Egyptian, 40 years later God called him to go back to Egypt and tell Pharoah to release the Israelites. Moses was on Mt. Sinai with God two different times for 40 days. Jesus was in the wilderness for 40 days. Does the #40 have a specific meaning?
Also, all the times that Moses was on the mountain with God, his face glowed with radiance only after receiving the second set of stone tablets with the Ten Commandments. Do you have any idea as to why this happen on this occasion?
The common thread running through the events you mentioned is that each was a period of testing. These and other similar events have caused the number 40 to become known as the number of testing.
During his second 40 day period on the mountain God and Moses became close enough so that when Moses asked God to see His Glory, God hid him in the cleft of a rock while He passed by (Exodus 33:18-23). After that his face was temporarily radiant. He wore a veil so people would not see the radiance fading, apparently worried that as the radiance faded people would wonder if his favor with God was diminishing. Each time he went into the tabernacle to speak with God the radiance was temporarily restored again. (Exodus 34:29-35) The radiance was a result of being in the close proximity of the Lord.