How is space and light used in the Oath of Horatii painting by Jacques-Louis David?

The "Oath of the Horatii"is a painting painted in 1784 and done in the Neoclassical style.  It depicts a scene from Roman legend where three men, brothers, salute toward three swords held up by their father as women behind them grieve.  

The space, like many works done in this style, is rigorously organized by the artist.  The arches and pillars in the background keep the viewer's attention fixed on the action in the foreground.  The arches...

The "Oath of the Horatii"is a painting painted in 1784 and done in the Neoclassical style.  It depicts a scene from Roman legend where three men, brothers, salute toward three swords held up by their father as women behind them grieve.  

The space, like many works done in this style, is rigorously organized by the artist.  The arches and pillars in the background keep the viewer's attention fixed on the action in the foreground.  The arches also serve to cut off the extension of space into the background, pushing the action of the scene forward in a manner similar to Roman relief sculptures.  Jacques-Louis David is clearly utilizing space to connect his painting to the Roman traditions of the past. 

Another way in which space is used is the father's clasped hands are placed over a vanishing point of the perspective scheme, which places strong emphasis on the hard lines and edges of the architectural setting. 

To discus the "light" element of this painting, some more context on the legend it is depicting is in order.  In the legend, the Roman Horatius family had been picked for a duel against three members of the Curiatii family, a duel from which only one of the three brothers survives.  This is where the light element in the painting becomes most prominent.  The brother who is depicted in the most direct light and is closest to the viewer is the sole survivor of the duel. His brothers, on the other hand, are depicted in low light and put in an obstructed view.  This deliberate decision is often viewed as a symbolic depiction of the other two brothers' deaths.

Another point you could note is how the darkness of the background serves to put the foreground figures into stronger contrast, thus serving as another way to draw the viewer's eye to the foreground.