# Focal point and normals

On Milnor's Morse theory, we have:

Given a manifold $$M\subset\mathbb{R}^n$$, let $$N=\{(q,v)~\vert~ q\in M,$$ $$v$$ is perpendicular to $$M$$ at $$q\}\subset M\times \mathbb{R}^n$$

And $$E:(q,v)\mapsto q+v$$.

A point $$e\in \mathbb{R}^n$$ is a focal point of a manifold $$M\subset \mathbb{R}^n$$ if $$e=q+v$$ for some $$(q,v)\in N$$ and the Jacobian of $$E$$ at $$(q,v)$$ has nullity $$>0$$.

My question is, Milnor claims that a focal point of M is a point in $$\mathbb{R}^n$$ where nearby normals intersect, how to see this claim?