Upon what incident was the verse related to hijab (tasattur) sent down?

Dear Brother / Sister,

The chapter of an-Nur, verse 30:

"Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: And Allah is well acquainted with all that they do."

The chapter of an-Nur, verse 31:

"And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husband´s fathers, their sons, their husbands´ sons, their brothers or their brothers´ sons, or their sisters´ sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! turn ye all together towards Allah, that ye may attain Bliss."

The reasons why the verses were sent down:

1. Ibn Mazdawi narrated the following from Ali b. Abi Talib:

«When the Messenger of Allah (pbuh) lived in Madinah, a woman and a man wandering in the streets of Madinah looked at each other when they came across. Benefitting from their gazes, Satan made them like each other. The man was both gazing at the woman and walking. Since his head faced the woman all the time, he hit a wall in front of him and his nose bled. «I swear by Allah that I will not clean the blood of my nose until I go to the Messenger of Allah (pbuh) and tell him about the incident.» He went to the Messenger of Allah (pbuh) and told him about the incident. The Messenger of Allah (pbuh) said, «Bleeding of your nose by hitting the wall is the penalty of your sin » Thereupon, the following verse was revealed: ‘Say to the believing men that they should lower their gaze...’» (Suyuti, Durrul-Manthur, 5/40)

2. Ibn Kathir, reports the following from Muqatil b. Hayyan who reports from Jabir b. Abdullah al-Ansari:

Asma b. Mirsad had a date orchard near the place called Bani Haritha. Women used to go there without wearing skirts and without covering their breasts, hair and anklets around their legs. Asma said, «How nasty your appearance is!» Thereupon, the following verse was sent down: ‘And say to the believing women that they should lower their gaze...’» (Ibn Kathir, Tafsir, 3/283. Suyuti. 5/104.)

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