Is it obligatory to wash inside the eye when doing wudoo’?
Question

                When doing wudoo’, should I wash inside the eye with water?
Praise be to Allah.
    It is not prescribed to wash inside the eye when doing wudoo’ 
    or ghusl; rather doing that is harmful to the eyes. 

    Imam ash-Shaafa ‘i (may Allah have mercy on him) said – 
    concerning the verse in which Allah, may He be exalted, says (interpretation 
    of the meaning): “When 
    you intend to offer As-Salat (the prayer), wash your faces and your hands 
    (forearms) up to the elbows” 
    [al-Maa’idah 5:6] –: I 
    do not know of any difference of opinion concerning the fact that the face 
    that must be washed when doing wudoo’ is the outward surface of the face, 
    not what is underneath; a man is not obliged to wash his eyes or sprinkle 
    water under his eyelids.

    End quote from al-Umm (1/40) 

    Ibn Qudaamah (may Allah have mercy on him) said: Some of our 
    companions stated that one of the Sunnahs of wudoo’ is to wash inside the 
    eyes, and that it was narrated from Ibn ‘Umar that he became blind because 
    he often made the water enter his eyes. Al-Qaadi said: Rather that is 
    encouraged in the case of ghusl. This was stated by Ahmad in several places. 
    That is because ghusl following sexual activity involves more extensive 
    washing, as it involves washing the entire body, and washing underneath 
    thick hair (so that the water reaches the skin), that which is beneath the 
    eyelids, and so on, and inside the eyes comes under the heading of parts of 
    the body that it is possible to wash. If it is not obligatory, then at least 
    it is encouraged (mustahabb). 

    However the correct view is that this is not Sunnah either in 
    wudoo’ or in ghusl, because the Prophet (blessings and peace of Allah be 
    upon him) did not do this or instruct anyone to do it, and it is harmful. 
    What is mentioned from Ibn ‘Umar indicates that it is nor right, because it 
    caused him to lose his sight, and doing anything that it is feared will 
    cause one to lose one’s sight or will damage it, when there are no reports 
    to indicate that it is prescribed, if it is not haraam then it is at least 
    makrooh.

    End quote from al-Mughni (1/77) 

    Based on that, it is sufficient to you to wash the face, 
    without getting water into your eyes. 

    And Allah knows best.