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)