The word hijab which is a noun comes from the root 'hajaba' which means to cover, shut out, hinder anyone from access. The word hijab itself means veil, curtain, screen, barrier. The term 'hijab' occurs in al quran about seven times in the following ayaat.

7:46 And between them is a barrier (hijabun), and on the elevated platform are men who recognized the people by their features. And they called out to the dwellers of Paradise: "Peace be upon you!" They have not yet entered it, but they are hoping.

17:45
And when you read the Quran, We place between you and those who do not believe in the Hereafter an invisible barrier (hijaban).

19:17
She took to a barrier (hijaban) which separated her from them, so We sent Our spirit to her, and he took on the shape of a human in all similarity.

33:53
O you who believe, do not enter the prophet's homes except if you are invited to a meal, without you forcing such an invitation. But if you are invited, you may enter. And when you finish eating, you shall leave, without staying for conversation. This used to annoy the prophet, and he was shy to tell you. But God does not shy away from the truth. And if you ask his wives for something, ask them from behind a barrier (hijabin). This is purer for your hearts and their hearts. And it is not for you to harm God's messenger, nor that you should marry his wives after him. This is indeed a gross offence with God.

38:32
He then said: "I enjoyed the good of materialism more than I enjoyed remembering my Lord, until it has become totally dark (hijabi)."

41:5
And they said: "Our hearts are sealed from what you invite us to, and in our ears is a deafness, and there is a barrier (hijabun) between us and you. So do what you will, and so will we."

42:51
And it is not for any human being that God would speak to him, except through inspiration, or from behind a barrier (hijabin), or by sending a messenger to inspire whom He wills by His leave. He is the Most High, Most Wise.

From the above ayaat one can clearly see that in the quran 'hijab' is not used for a dresscode. There is no order whatsoever for a female to wear 'hijab' or 'headscarf' over her head. Another mistaken ayat is
33:59 where people somehow associate the word 'jalabib' with wearing a headscarf or mandatory 'hijab'. This word simply means over-garments.

33:59 O prophet, tell your wives, your daughters, and the wives of the believers that they should draw their cloaks (jalabeeb) about themselves. That is better so that they would be recognized and not harmed. God is Forgiver, Merciful.

This is simply telling the believing women to wear garments appropriate for outside, something modest according to
24:31 which now brings me to the subject of 'khimar'.

Khimar is the plural form of khumur (24:31), it means cover, screen, or head veil. The root of this word is 'khamara' and in al quran two derivatives are used, khamar (any intoxicating thing) and khumur. Note the theme of these words including the root deal with 'covering' something. Khamara means to cover, conceal, viel, hide, anything that clouds or covers the intellect (this includes all substances that are intoxicating). In
24:31 we have the order that women should place their covers over their chests. There is nothing suggesting drawing a viel over one's head or covering everything except their face and hands. 

24:31 And tell the believing women to lower their gaze and keep covered their private parts, and that they should not show-off their beauty except what is apparent, and let them place their covers (khumur) over their chests. And let them not show-off their beauty except to their husbands, or their fathers, or fathers of their husbands, or their sons, or the sons of their husbands, or their brothers, or the sons of their brothers, or the sons of their sisters, or their children that come after them, or those who are still their dependants, or the male servants who are without need, or the child who has not yet understood the composition of women. And let them not move their hips in a manner that reveals what they are keeping hidden of their beauty. And repent to God all of you believers that you may succeed.

Other instances of the derivatives of khamara can be found in 2:219, and 5:90, 91.

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