How is a telescope’s light-gathering power related to its aperture diameter?

A telescope’s light-gathering power is directly determined by the diameter of its aperture—the clear objective lens or mirror that collects incoming light.1

The relationship is defined by the ratio of the diameters squared. Because the area of the circular aperture increases with the square of its diameter, a telescope with a larger aperture collects significantly more light than one with a smaller aperture. For example, an objective with a 25-cm diameter will collect four times the light of a 12.5-cm objective, as calculated by the ratio of their diameters squared: $(25\times 25)÷(12.5\times 12.5)=4$.1

By increasing the aperture size beyond that of the human pupil, telescopes can capture light from much fainter and more distant objects, such as stars, nebulae, and galaxies. Consequently, the ability to collect more light is considered the most important power of an optical telescope.21