Similarity of Circles

Every year, trees grow outward, and this can be visualized by the rings in their cross-sections. Every new ring (see above) represents another outer layer of the tree; thus, the spaces between the rings are the total growth that a tree had during one year of growth, meaning that a tree's age can be determined by counting the number of rings it has.

Suppose a tree is $n$ years old. How many similar circles will there be in its cross-section?