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` compared to `B` ? Show that range of `A` is three times the range of `B`.

Explanation

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 Als 9 times that of B.
Now, range tells us how far away a star of some standard brightness can be spotted by the telescope.
As intensity `propto(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.