Find the longest possible path in full binary tree
If it is a full binary tree, that is defined as:


  Full binary tree is a tree in which every node other than the leaves has two children. 


Then you know the depth $D$ will be half of the total possible diameter. This is because we can take a maximum possible path of length $D$ from root to any leaf in the subtree rooted at the left-child of the root, and we can also take a maximum possible path of length $D$ from root to any leaf in the subtree rooted at the right-child of the root. Thus, adding these up would be a path of length $2D$. 

Thus, we get that the maximum possible diameter would be equal to twice the depth (i.e. $\mathrm{diameter} = 2\cdot \mathrm{depth}$).