Is it permissible for a sister to show her brother a picture of a girl without hijab, and without the girl's knowledge, so that her brother may see her hair before proposing to her?

The basic principle for someone who wishes to propose to a woman is to see her directly. It is prohibited to send her picture to him due to potential harms. However, if these harms are safeguarded against, it is permissible to look at her picture, under certain conditions:

1. You must be firm in your intention to propose. 2. The picture must show only the woman's face and hands, and what is customarily uncovered in front of maharim (unmarriageable kin). 3. The viewing must be through a trustworthy intermediary; it is not permissible for the woman to send her picture directly. 4. The matter is limited to viewing the picture, with permissibility to repeat the viewing, but the suitor is not allowed to keep it. 5. No man other than the suitor should see this picture.

The girl's permission is not required for him to see her or her picture. Nonetheless, seeing the woman directly remains the original and preferred method, as a picture may not accurately represent reality.