All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The majority of the scholars are of the view that when a person joins the Imaam while in Rukoo’ and he bows down for that Rak’ah until he stays still before the Imaam raises up his head from Rukoo’, then this is considered a valid Rak’ah for him (i.e. he should count this Rak'ah as one Rak'ah).
There is much evidence about this among which are the following:
Abu Hurayrah narrated that the Prophet said: "When you come to the prayer and find us in the position of prostration, you should prostrate with us but do not consider it as a Rak'ah, and whoever joins us in prayer while in Rukoo' (bowing down position) then he has indeed reached the prayer (i.e. his Rak’ah is valid)." [Abu Dawud and Ibn Khuzaymah]
The meaning of the Hadeeth is that if someone joins the prayer while the Imaam is in prostration, he prostrates with the Imaam but he does not count it as Rak’ah, and if he joins the prayer while the Imaam is in Rukoo', he bows down (makes Rukoo') and counts it as a Rak’ah as he has reached the Imaam while the latter is in Rukoo'.
The evidence about this context is supported by the narration of Imaam Ahmad of the same Hadeeth, with the following addition: "Whoever reaches the Rukoo’, he has indeed reached the Rak’ah."
The other evidence is the Hadeeth reported by Al-Bukhari and narrated by Abu Bakrah that he reached the Prophet while in Rukoo’, and he performed the Rak’ah (bowed down) before reaching the row (of the people standing in line in prayer). Thereupon, the Prophet told him, "May Allaah increase your zeal, but do not do that again (meaning do not bow down before reaching the row)."
So the evidence from this Hadeeth is that he reached the Prophet while in Rukoo’, and as he feared that he would miss the Rak’ah, he made Rukoo’ (bowed down) before reaching the row so that he would not miss it (Rak’ah), and as the Prophet did not order him to make up the Rak’ah, then this is a confirmation that it is sufficient (and valid).
Allaah Knows best.