Here's why:

* Resolving power refers to the ability of an optical system to distinguish between two closely spaced objects. It's essentially the smallest distance between two points that can be seen as separate.

* Numerical aperture is a measure of the light-gathering ability of a lens. A higher NA means the lens can collect more light from a wider cone of angles.

The relationship:

The resolving power (RP) is inversely proportional to the wavelength of light (λ) and directly proportional to the NA:

RP = λ / (2 * NA)

This means:

* Higher NA = Higher resolving power: A larger NA allows the lens to collect more light and focus it more tightly, resulting in a smaller spot size and a better ability to resolve fine details.

* Shorter wavelength = Higher resolving power: A shorter wavelength of light allows for better resolution because the diffraction effects that limit resolution are reduced.

Example:

Microscopes with high numerical aperture objectives are able to resolve finer details than those with lower NA objectives. This is why oil immersion objectives (which have higher NAs) are often used in microscopy to achieve the best possible resolution.