Praise be to Allah.
There is no text in the Sunnah – as far as we know – which states where the worshipper should look when saying the salam at the end of the prayer. What is narrated in Saheeh Muslim is that he should turn towards the person who is beside him.
It was narrated that Jaabir ibn Samurah (may Allah be pleased with him) said: I prayed with the Messenger of Allah (peace and blessings of Allah be upon him) and when we said the salam we said with our hands, “Al-salamu ‘alaykum, al-salamu ‘alaykum.” The Messenger of Allah (peace and blessings of Allah be upon him) looked at us and said, “Why do you gesture with your hands like the tails of spooked horses. When one of you says salam, let him turn to his companion and not gesture with his hand.” Narrated by Muslim, 421.
“Spooked horses” refers to nervous horses that will not settle down.
There is also a report which indicates that one should turn far to the right and left.
It was narrated from ‘Aamir ibn Sa’d that his father said: I used to see the Messenger of Allah (peace and blessings of Allah be upon him) saying the salam to his right and left, turning so far that I could see the whiteness of his cheek. Narrated by Muslim, 582
Al-Nasaa’i (1329) narrated from ‘Abd-Allah ibn Mas’ood (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) used to say salam to his right, “Al-salamu ‘alaykum wa rahmat-Allah,” until the whiteness of his right cheek could be seen, and to his left, “Al-salamu ‘alaykum wa rahmat-Allah,” until the whiteness of his left cheek could be seen. Classed as saheeh by al-Albaani in Saheeh al-Nasaa’i.
That cannot happen unless one turns a long way, as al-Kasaani said in Badaa’i’ al-Sanaa’i’, 1/214.
What we learn from these ahaadeeth is that the worshipper should turn to his right and left, and he should turn a long way, towards those who are on his right and left, and he may look at his neighbour or at his shoulder; the matter is broad in scope.
And Allah knows best.
Comment