وَٱلشَّمْسِ وَضُحَىٰهَا
Root sh-m-s. The word counts as feminine in Arabic; it is the first referent of all the هَا pronouns that come through the sūra.
The sun occurs in some thirty places in the Qurʾān, and almost every time it stands in a context of order and measure: "The sun and the moon move by a reckoning (ḥusbān)" (al-Raḥmān 55/5); "It is He who made the sun a light and the moon a brightness… and determined stations for it, that you might know the number of the years and the reckoning" (Yūnus 10/5). In the Qurʾān's description of nature the sun is not an element of warmth or of beauty; it is first of all a clock.
Against this, the sun is one of the objects the Qurʾān forbids worshipping: "Do not prostrate yourselves to the sun or to the moon; prostrate yourselves to God, who created them" (Fuṣṣilat 41/37). In the account of Sheba a people is described as prostrating themselves to the sun (al-Naml 27/24). That is: when an oath is sworn by the sun, it is spoken on a cultural ground where worshipping that same sun is forbidden. An oath is an exaltation, but it shuts the door on worship: the difference between the one who swears and the thing sworn by is exactly the difference between the Creator and the created.
Root: ض-ح-و. Its concrete sense is to be open to the sun, to be out under the sun. Ḍaḥā is the lifting of shade and the opening of a place to the light. From the same root ادَّاحَى/ضَاحِيَة — a place left in the open, without shade.
In the Qurʾān this sense occurs once in its bare form, in the description of the Garden: "there you shall not go hungry, nor go naked; there you shall not thirst, nor be left in the sun (lā taḍḥā)" (Ṭāhā 20/118-119). The verb here means directly "to be scorched under the sun". Under the root, then, lies not the pleasantness of light but the nakedness of light: being left without cover.
As the name of a time, ḍuḥā is the forenoon, when the sun has climbed and the light has spread fully — the early vagueness of morning is past, the steepness of noon has not yet come. The hour when shadows have shortened and everything is seen at its clearest.
Why, then, "the sun and its forenoon"? After an oath has been sworn by the sun, swearing further by its forenoon looks at first like surplus. It is not. The sun is a body; the forenoon is the result of that body's work. The oath is sworn both by the source and by the state the source produces. This is the first instance of the logic that runs on through the sūra: a thing and the condition that thing brings out are named together.
And there is this too: the sūra sets up the theme of "bringing out into the open" in its very first verse. Ḍuḥā is the time when the covering is lifted. Ten verses later, deliverance will be described with zakkāhā (he purified it and made it grow, he brought it out) and loss with dassāhā (he buried it, he hid it). From its first word the sūra carries the tension between being in the open and being concealed.