The juxtaposition of anatomy and physics in the eye

People are quick to accept the assumption that a light will appear dimmer the farther away they are, citing the inverse square relationship that illuminance obeys as rationale. As a result, there are no studies that actually intend to verify this argument, given that the reasoning appears quite solid. However, repeated observations of light sources maintaining their brightness over large distances prompted us to explore how the brightness, or perceived illuminance of a light varies with the viewing distance from the object. When examining the anatomy of the eye, we found that the image it produces also decreases according to the inverse square of the viewing distance. Thus, we hypothesized that since both the illuminance of the light source and image size decrease at the same rate, then the concentration, or intensity of the image remains unchanged, and subsequently the perceived illuminance. To test our hypothesis, a circular light source was placed in line with a biconvex lens and light sensor, and the illuminance of the resulting image was measured at distances between 2–17 meters. We found that the illuminance of the image of light remained constant for most of the distances. Furthermore, the illuminance of the image increased at first before approaching that stable maximum. From our results, we concluded that our hypothesis was correct, and the decreasing image size indeed neutralizes the decreasing illuminance of the source. Beyond challenging previously held beliefs, our findings also have some niche aesthetic and economic implications for light fixture manufacturers.