Two convex lenses of same focal length but of paerture `A_(1)` and `A_(2)(A_(2) lt A_(1))` are used as the objective lenses in two astronomical telescope having identical eye pieces. What is the ratio of their resolving power ? Which telescope will you prefer and why ? Give reason.

Explanation

As is known, `R.P = (D)/(1.22 lambda)`, which varies directly as aperture `D` of objective lens.
Therefore, `(RP_(1))/(RP_(2)) = (A_(1))/(A_(2))`
As `A_(2) lt A_(1)` or `A_(1) gt A_(2)`, therefore, the first astronomical telescope (with aperture `A_(1)`) has higher resolving power than the second astronomical telescope (with aperture `A_(2)`). Obviously, we shall perfer to use the first astronomical telescope.