Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh
In the Name of Allah, the All-Merciful, the Mercy-Giving
All praise is due to Allah. Peace and blessings be upon His Messenger Muhammad.
In principle, it is not permitted for a Muslim woman to uncover her hair and ears in front of non-mahram men. Cases of necessity entail concession. But the concession is restricted to actual necessity, which means in this case:
1- There has to be an actual necessity to have a passport. Travelling for hajj and medical treatment are examples of necessity, while travelling for tourism is not.
2- A Muslim woman has to be careful to uncover only the parts of her head required for identification as required by authorities.
3- If there is a woman or a mahram man who can take this photo, a non-mahram man is not allowed to take it. Modern digital cameras have made it easy to for anyone to take a photo. If, supposedly, there is no one who can take the photo except a non-mahram man, that will be another instance of necessity and a concession follows.
Almighty Allah knows best.
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