Let $M$ be a complete riemannian manifold, $L$ a smooth submanifold of $M$ and $\gamma$ a geodesic with $\gamma'(0)$ normal to $L$. A focal point of $L$ is a critical value of the normal exponential $\exp:\nu L\to M$. So the question is: is the set of focal points $\gamma(t)$ of $L$ discrete?

I know that's related to the Morse index theorem, but all the versions of it I've found are too general and do not contain a conclusion about finiteness.