7.5. Size/Distance Relationships

Our perception of an object’s size depends on both its retinal image size and its perceived distance from us. When an object is far away, it produces a small retinal image; when close, it produces a large one. Our brain combines two pieces of information: the size of the object on the retina (visual angle) and depth perception cues (including binocular disparity) to estimate distance and make judgments about actual object size.

Sometimes estimating distance is challenging. For example, the sun and moon create similarly sized retinal images in the sky, but the sun’s diameter is actually about 400 times larger than the moon’s. We perceive them as similar in size because it’s difficult to judge their vastly different distances from Earth – the sun is much further away than the moon.

Emmert formulated a size-distance scaling equation that shows how perceived size results from combining retinal image size and perceived viewing distance:

S = k(R × D) Where: S = perceived size R = retinal image size D = perceived distance of the object

This relationship is clearly demonstrated by afterimages. If you look at a bright light bulb and then close your eyes, you see an afterimage. This afterimage appears small when viewed against a nearby surface but large when viewed against a distant surface. Afterimages occur due to adaptation or bleaching of retinal cells. While the retinal image size (R) of the afterimage remains constant, the perceived size (S) changes with the perceived distance (D) of the surface you’re looking at. This phenomenon is known as Emmert’s Law.

Size Constancy

The size-distance scaling equation explains our perception of size constancy in everyday environments. For example, in the photograph of people on stairs (Figure 7.13), those at the bottom appear larger than those at the top, but we don’t assume they’re giants – we understand they’re simply closer to us. Similarly, when people walk up stairs, their retinal image gets smaller, but we don’t perceive them as shrinking – we understand they’re maintaining constant size while moving further away.