Which binocular cue for perceiving depth involves the extent to which the eyes converge when looking at an object?

The cue for perceiving depth that involves the extent to which the eyes converge when looking at an object is convergence. This physiological response occurs when the eyes turn inward to focus on a nearby object. The brain uses the degree of convergence as one of the cues to determine the distance of the object from the viewer. When an object is closer, the eyes must converge more sharply, and the brain interprets this increased convergence as a sign that the object is nearer.

The other options refer to different depth cues: divergence refers to the eyes moving away from each other when looking at distant objects; accommodation involves the lens of the eye changing its shape to focus on objects at different distances; and binocular disparity involves the slight difference in images received by each eye due to their horizontal separation. While all of these cues contribute to depth perception, convergence specifically relates to the inward movement of the eyes and is key to judging distance for objects that are relatively close.