## Maximum Resolving Power Calculator

The maximum resolving power of a telescope refers to its ability to distinguish fine details or separate closely spaced objects in the observed image. In other words, it determines how much fine detail the telescope can reveal. Resolving power is primarily determined by the size of the telescope's aperture (the diameter of its objective lens or primary mirror) and the wavelength of the light being observed.

**Dawes Limit**

The Dawes limit, also known as Dawes' criterion, is a formula that provides an estimate of the maximum resolving power of a telescope. It determines the smallest separation between two point sources of light that can be resolved as distinct objects in the telescope's image. The formula is as follows:

**θ = 11.6 / D**

In this equation, θ represents the angular resolution in arcseconds and D is the diameter of the telescope's aperture in millimetres.

For example, if a telescope has an aperture diameter of 200 mm, you would substitute D = 200 into the equation:

θ = 11.6 / 200 = 0.058 arcseconds

This means that, under ideal conditions, the telescope would be capable of resolving objects separated by approximately 0.058 arcseconds.

**Rayleigh's Limit**

The Rayleigh criterion is a widely used formula that provides an estimate of the maximum resolving power of a telescope. It determines the smallest separation between two point sources of light that can be resolved as distinct objects in the telescope's image. The formula is as follows:

**θ = 1.22 * (λ / D)**

To calculate the maximum resolving power using the Rayleigh criterion, you need to know the wavelength of the light being observed and the diameter of the telescope's aperture. Let's consider an example:

Suppose we have a telescope with an aperture diameter of 200 mm and we want to calculate the maximum resolving power for visible light, which has an approximate wavelength of 550 nm (0.55 μm). Before performing the calculation, we need to convert the wavelength to the same unit as the aperture diameter (millimeters). Since 1 μm is equal to 1,000 nm, the wavelength becomes 0.55 μm = 550 nm = 0.55 mm.

θ = 1.22 * (0.55 mm / 200 mm)

θ = 1.22 * 0.00275

θ = 0.003355 radians

To convert the angular resolution to arcseconds, you can use the conversion factor of 1 radian ≈ 206,265 arcseconds:

θ = 0.003355 radians * 206,265 arcseconds/radian

θ ≈ 0.692 arcseconds

This means that, under ideal conditions, the telescope would have a maximum resolving power of approximately 0.692 arcseconds, allowing it to distinguish objects separated by that angular distance.

θ = 1.22 * (0.55 μm / 200 mm)