All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Washing the feet is a mandatory act of Wudu`, and, in this regard, the basis is the washing itself, because Allah the Almighty says {What means}:" O ye who believe! when ye prepare for prayer, wash your faces, and your hands (and arms) to the elbows; Rub your heads (with water); and (wash) your feet to the ankles." {Al-Ma`idah, 6}.
Sharia has permitted wiping over the Khuffs (socks made from thick fabric or leather), as mentioned in the authentic narrations. It was reported on the authority of Sa`id Bin Abi Waq-qas that "The Prophet (Peace and blessings be upon him) wiped over his Khuffs" {Related by Bukhari}. In addition, there are many other narrations supporting this practice. In principle, it is lawful to wipe over the Khuffs or what is similar to them.
However, it is permissible to wipe over the socks under the condition that they are strong, durable, and waterproof. Ibn An-Naqeeb, a Shafie scholars, said: "It is permissible to wipe over the Khuffs….It is conditioned that they are put on after the complete Wudu', be in state of ritual purity, they cover the feet and the ankle, they are waterproof, and durable for walking; be they made from leather, fabric, or other material." {Umdat Assalik, P.30}.
Ibn Hajar (May Allah have mercy on him) said: "It doesn`t avail a person to wipe over woven socks that are non-waterproof, even if they are strong and durable for walking-according to the reliable opinion of the Shafie School of thought-because they don`t have the characteristics of Khuffs mentioned in the texts of Sharia." {Tohfat Al-Mohtaj, Vol.1:P.252}.
In conclusion, if the socks are thin, it doesn`t avail a person to wipe over them, because they don`t meet the above conditions. Consequently, the feet must be washed, and it is more appropriate to be on the safe side when it comes to acts of worship to be cleared from liability before Almighty Allah. And Allah the Almighty knows best.