Why is it that the bigger the...

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Why is it that the bigger the telescope (or the thicker the tube), the more light power it gathers?
Think of light originating from celestial bodies as a wide, infinite stream. Now, if a village or city wants to take water from a river, the people have to place a pipe in the river to divert water to the village. The larger the population, the more water is needed, and a larger-diameter pipe has to be used. The larger the pipe, the more water is collected. The same holds true for a telescope: The bigger its diameter, the more it gathers of the stream of light, delivering it to the observing astronomer.