My answer to the question, "effect of fiber optic on NA" was deleted with the reason given being, "Please don't post complete answers to the underlying problem in homework-like questions."
I believe this was an incorrect decision on two grounds:
This isn't a homework-like question. A homework-like question is one where there is one correct answer, which can be calculated from given parameters, and knowledge that can be contained in a single chapter of a textbook.
In particular, the question asks for a numerical answer (the NA of the output beam) without giving sufficient information to calculate it.
In this case, the answer is "it depends..." with some explanation of what it depends on.
Possibly this is a question that OP came up with while writing up lab work, and realizing they had done some of the lab incorrectly. But it isn't the kind of question with a single correct answer that we should consider to be "homework-like".
My answer is not a "complete answer".
The complete answer OP will need to complete their homework or lab write-up depends on information they (correctly) didn't even include in the posted question. For example, the diameter of the fiber core, and how the fiber was arranged in their experiment.
The answer is certainly not what an instructor would expect as a complete answer if they had, for some reason, assigned this question as homework.
Edit For those who can't see deleted answers, my answer was
A 810 nm multimode light source with 0.1 NA is launched into 3 m of multimode fiber whose NA is 0.2...What is the NA of the light exiting the fiber?
Most likely, it's about 0.2.
It could be lower, if the launch into the fiber is made carefully, and the fiber is kept very straight and unstressed so that light launched into one mode doesn't couple much into other modes.
If the fiber is twisted and/or curved multiple times along its length, the modes will be well mixed and the output beam will have NA of 0.2.
Does the length of the fiber affect the NA of the light exiting the fiber?
A very short length of fiber (say a few cm or 10's of cm) will not allow much mode mixing, and the output beam is more likely to be closer to the NA of the input beam.
Again this also depends on exactly how the input beam is launched into the fiber.