dynamic cast and static cast in C

Question

 I'm perplexed by the dynamic cast keyword in C++.

struct A {
    virtual void f() { }
};
struct B : public A { };
struct C { };

void f () {
    A a;
    B b;

    A* ap = &b;
    B* b1 = dynamic_cast<B*> (&a);  // NULL, because 'a' is not a 'B'
    B* b2 = dynamic_cast<B*> (ap);  // 'b'
    C* c = dynamic_cast<C*> (ap);   // NULL.

    A& ar = dynamic_cast<A&> (*ap); // Ok.
    B& br = dynamic_cast<B&> (*ap); // Ok.
    C& cr = dynamic_cast<C&> (*ap); // std::bad_cast
}