Light Gathering Area and Power

The light-gathering power of optical devices like telescopes, cameras, and even your eyes, depends on the light-gathering area of the object. Yes I said area - the greater the area of the opening, the more light gathered. You can think of these objects as light-buckets that are used to catch photons of light.

Let the circles below represent the mirror or lens in a telescope. The size can be specified by the diameter or radius of the circle. Remember that the radius is one half the diameter. The area of a circle is usually given in terms of its radius R, Area = $area$ . The area can also be given in terms of its diameter D, Area = ¼ $area2$ .
radius of circle

Light-Gathering Area= $area$ = ¼ $area2$

The light-gathering area of a 200 cm diameter mirror is: A = ¼ $area2$ = ¼ $pi$ (200 cm) ² = 31,416 cm²

How does the light-gathering area of a 400 cm diameter mirror compare? A = A = ¼ $area2$ = ¼ $pi$ (400 cm) ² = 125,664 cm²
It is much greater! You may have thought that since the diameter is doubled that the area would also double - but notice that the area is 4 times larger.

diameter is 400 cm

Light-gathering poweris a comparison of two light-gathering areas. Perhaps two different telescopes are compared or a telescope is compared to a human eye.

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Let's calculate the Light-gathering power of the 400 cm diameter mirror as compared to the 200 cm diameter mirror.

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This simply means that the 400 cm diameter telescope can gather 4 times as much light as the 200 cm diameter telescope. More light means more information and perhaps more detail.