✅Answer: Please pay attention to the following narrations:

1 عَنْ عَلِيِّ بْنِ مُحَمَّدٍ عَنْ بَعْضِ أَصْحَابِنَا عَنْ مَرْوَكِ بْنِ عُبَيْدٍ عَنْ بَعْضِ أَصْحَابِهِ عَنْ أَبِي جَعْفَرٍ قَالَ: قُلْتُ لَهُ إِنِّي إِمَامُ مَسْجِدِ الْحَيِّ فَأَرْكَعُ بِهِمْ فَأَسْمَعُ خَفَقَانَ نِعَالِهِمْ وَ أَنَا رَاكِعٌ فَقَالَ اصْبِرْ رُكُوعَكَ وَ مِثْلَ رُكُوعِكَ فَإِنِ انْقَطَعَ وَ إِلَّا فَانْتَصِبْ قَائِماً.

📚Al-Kafi, Vol. 3, p. 330

One of the companions said: I said to Imam Baqir (peace be upon him): I am the Imam of the congregation of the tribe's mosque. So I go into ruku' with them and I hear the shuffling of their shoes while I am in ruku'. (What should I do)?

The Imam said: Wait for a normal ruku' and a ruku' like your own (i.e., double the normal amount). So if they catch up with the prayer, so be it, and if not, straighten up (raise your head from ruku').

2 عَنْ أَحْمَدَ بْنِ مُحَمَّدِ بْنِ عِيسَى عَنْ مَرْوَكِ بْنِ عُبَيْدٍ عَنْ أَحْمَدَ بْنِ النَّضْرِ عَنْ عَمْرِو بْنِ شِمْرٍ عَنْ جَابِرٍ الْجُعْفِيِّ قَالَ: قُلْتُ لِأَبِي جَعْفَرٍ إِنِّي أَؤُمُّ قَوْماً فَأَرْكَعُ فَيَدْخُلُ النَّاسُ وَ أَنَا رَاكِعٌ فَكَمْ أَنْتَظِرُ فَقَالَ مَا أَعْجَبَ مَا تَسْأَلُ عَنْهُ يَا جَابِرُ- انْتَظِرْ مِثْلَيْ رُكُوعِكَ فَإِنِ انْقَطَعُوا وَ إِلَّا فَارْفَعْ رَأْسَكَ.

📚Al-Tahdhib, Vol. 3, p. 48

Jabir Ju'fi said: I lead a people in prayer, so I go into ruku' and people enter while I am in ruku'. How long should I wait? (How much can I prolong the ruku' so they can catch up with the prayer)?

The Imam said: How strange is what you are asking about, O Jabir!

Wait for twice the duration of your ruku', so if they catch up, then they have caught up, and if not, raise your head (from ruku').

✅It is clear that regarding the question mentioned, the Imam of the congregation waits for a maximum of twice the duration of his normal and usual ruku', and if some people still do not catch up, he should not delay any longer and should raise his head from ruku'.

The amount of prolonging the Imam's ruku'

اللَّهُمَّ فَصَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ