Is there a specific requirement for the thickness or width of the Sutrah?

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There is no known fixed limit regarding the thickness or thinness of the Sutrah. It is permissible for the barrier to be thin, such as a spear (sahm) or a lance (harba), or thick, such as a wall. The Prophet, peace be upon him, used to take the 'anazah (a short spear) as a barrier. Abu Sa'id reported that they used the arrow and the stone for taking a barrier in prayer.