1. One who bows down during the Amidah (in those four places where Chazal decreed) must bow down until all of the vertebrae in his spinal column protrude. He must make sure that he bows not only with his body but also with his head (he should bend it down). However, he should not bow down too far, to the extent that his mouth will be at the level of his belt, as this is being arrogant in that he is being too stringent on himself. (Shulchan Aruch and Mishne Berurah 113)

2. For an old or ill man, who is unable to bend down so much, it suffices that he lowers his head slightly, so that it is obvious that he wants to bow down but is unable to do so. (ibid)