The main Worry for female travelers to Iran is regard to wearing hijab or Islamic customs but let us to make it more clear for you,
In modern Iran the Islamic dress code for ladies is very different to other Arabic and Islamic countries, it doesn't mean that it is harder or easier .
the ladies should follow some modern Islamic Costumes in public ( this is not about your private space) , what is this ?
what to wear doesn't have a certain criteria in fact, Iran current government introduced and suggested a pattern as the best wearing for ladies in public and it is chador ( very large and wide cloth like climbers Pancho in black ) but people and travelers are not obligated to obey this suggestion except governmental staffs, there is a min. scale to be OK ;
Women should cover her self with no Stretched Clothes EXCEPT your face, ears and a half part of your hair that could be uncovered, your hands and lower arm area too, regard to legs you can wear jeans or no Stretched Skirt also as a over dress for bust wear something like coat as long as to cover your hips.
Having mentioned factors are necessary in maximum scale in Airport and mosques.
There are some exceptions and occasions that you can remove the Islamic dress when during the trip you can ask your guide about it .
Wearing Slippers or sandals with no socks are OK in Nature, Street, Bazaar, Touristic sites .
It is recommended to wear Sport Shoe in Airport for entering and leaving Iran.
Have a look at below images to became more familiar with ladies dress in the public.