The lens of human eye has a diameter of `0.8 cm`. How much fainter star can be seen through `508 cm` objective of an astronomical telescope at Mount Polomar in USA ?

Answer

`403, 225`

Explanation

Here, `d = 0.8 cm, D = 508 cm`
As light gathering power `prop ("diameter")^(2)`.
`:.` Brightness ratio `beta = (D^(2))/(d^(2)) = ((508)^(2))/((0.8)^(2)) = 403, 225`
It implies that the telescope can see a star `403, 225` times fainter than the faintest star that can be seen with naked eye.