To determine the resolving power of a microscope, you can use the formula:

$RP = \frac{\lambda}{2 \, \text{NA}}$

The resolving power (RP) of a microscope is a measure of its ability to distinguish between two closely spaced objects. This capability is influenced by both the wavelength of light employed and the numerical aperture (NA) of the objective lens. Specifically, a shorter wavelength and a larger numerical aperture will yield a higher resolving power.

The formula for calculating the resolving power is:

$RP = \frac{\lambda}{2 \, \text{NA}}$

Here, $RP$ represents the resolving power, $\lambda$ is the wavelength of the light being used, and NA is the numerical aperture of the objective lens. The resulting value is expressed in units of distance, typically nanometers (nm).

For instance, consider a microscope that utilizes green light with a wavelength of $550 \, \text{nm}$ and features an objective lens with a numerical aperture of $0.95$. The resolving power can be calculated as follows:

$RP = \frac{550}{2 \times 0.95} = 289.47 \, \text{nm}$

This indicates that the microscope is capable of distinguishing between two objects that are at least $289.47 \, \text{nm}$ apart.

It is important to recognize that the resolving power represents a theoretical limit, which may not always be attainable in practical applications due to various factors such as optical aberrations and diffraction. Nevertheless, it serves as a valuable metric for assessing the performance of a microscope and can guide the selection of the appropriate instrument for specific applications.