When I type
(Eq.\ref{eq.15})
The output is

Obviously the spacing between "Eq." and "1.15" is too closed.
But when I type (adding a space)
(Eq. \ref{eq.15})
The output is:

Obviously the spacing between "Eq." and "1.15" is too wide!
My question is how I can get appropriate spacing.

Eq.~\ref{eq.15}is the correct input for two reasons: the space is not “end of sentence” and no line break can happen at that space. – egreg Jun 19 '15 at 19:36