It’s a sunnah reading surat Al-Kahf on Friday night or in the day of Friday. The Friday night starting with the sundown on Thursday. This opportunity ends until the sundown on the day of Friday. From this it can be concluded that the opportunity to read surat Al-Kahf is from sundown Thursday afternoon until sundown on Friday.
From Abu Sa'id al-Khudri ra,
من قرأ سورة الكهف في يوم الجمعة أضآء له من النور ما بين الجمعتين
"Whoever reads Surah al-Kahf on Friday, then will be emitted lights for him between the two Fridays." (Narrated by al-Hakim: 2/368 and Al-Bayhaqi: 3/249).
Ibn Hajar commented on this hadith in al-Adzkar Takhrij, "hasan hadeeth." He stated that this hadith is the hadith most powerful about surah Al-Kahf in Sahih al-Jami', no. 6470.
Imam al-Shafi'i rahimahullah in Al-Umm stated that reading surah Al Kahf, can be performed on Friday night and noon based on the narrated of it. (Al-Umm, Imam al-Shafi'i: 1/237).
Ibn Hajar Al-Hafidzh rahimahullaah said in his Amali: Thus are the narrated who using the word "day" or "night" Friday. It can be concluded that the "day" means the night. Likewise, "night" is a Friday night and afternoon. (See: al-Qadir Faidh: 6/199).
Dr. Muhammad Bakr Isma'il in Al-Fiqh al Wadhih min al Kitab wa al Sunnah mentions that among the good deed recommended to do on the night and day Friday was reading surah Al Kahf, as hadeeth quoted above. (Al-Fiqhul Wadhih minal was Sunnah Book, page 241).
From some of the history above, the rewards are prepared for those who read surah Al-Kahf on Friday night or during the day will be given a light (irradiated). And the light is given on the Day of Judgment, which extends from the bottom of his feets up into the sky. And it shows the length of the distance light given to him, as the word of Allah Ta'ala:
يوم ترى المؤمنين والمؤمنات يسعى نورهم بين أيديهم وبأيمانهم
"On the day shalt thou see the believing men and the believing women- how their light runs forward before them and by their right hands as their light was shining in front and to the right of them." (Surah al-Hadid: 12)
The second reward to the person who reads Surah al-Kahf on Friday is given forgiveness of sins between the two Fridays. And perhaps this is what means, illuminated between the two Fridays. Because Nur (light) of loyalty will eliminate the darkness of immoral observance, as the word of Allah Ta'ala:
إن الحسنات يذهبن السيئات
"For those things, that are good remove those that are evil." (Surah Huud: 114)