You are treated like a plebe when you start the walk towards Alumni Hall on Iday, once you walk though those doors...game on! Some say you are a plebe until Herndon, others say it's when you see the chapel dome upon return of your summer cruise.
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I guess I should clarify, Herndon is in May. So, you are a plebe for almost an entire year!
Wow, I'm not an expert but maybe this will help answer your question. When I addressed mail to my son (even during plebe summer) it has always been sent as:
MIDN 4/c
But what exact moment on Iday that you become a Mid....I do not know.
You are definitely treated as a plebe as you walk through the doors....motivation by detailers and all!
When your plebe gets his/her ID card, it will state the rank is Midshipman. BTW, this is one of many features of the USN that is carried over from the British Navy.