What will be the ratio of the resolving powers of two convex lenses used as objective lens in astronomical telescope, having same focal length and apertures as `A_1 and A_2 (A_1 > A_2)`? Which telescope will you prefer and why?

Explanation

To solve the problem regarding the ratio of the resolving powers of two convex lenses used as objective lenses in an astronomical telescope, we can follow these steps:

### Step 1: Understand the Concept of Resolving Power
The resolving power of a telescope is defined as its ability to distinguish between two closely spaced objects. It is inversely proportional to the angular separation between the two objects that can be resolved.

### Step 2: Establish the Relationship
Resolving power (R) is directly proportional to the aperture (A) of the lens. This can be mathematically expressed as:
\[ R \propto A \]
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