The objective of telescope `A` has a diameter `3` times that of the objective of telescope `B`. How much greater amount of light is gathered by `A` compound to `B` ? Show that range of `A` is three times the range of `B`.
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As diameter of objective of `A` is `3` times that of `B`, its area of cross section is `9` times that of `B`. Therefore, light gathering capacity of `A` is `9` times that of `B`. Now, range tells us know far away a star of some standard brightness can be spotted by the telescope. As intensity `prop (1)/(("distance")^(2))` therefore, when distance of star is `3` times, the intensity would reduce to `(1)/(9)th`. As light gathering capacity of `A` is `9` times that of `B`, the star whose distance is `3` times can just be seen by A. Hence range of `A` is three times that of `B`.
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