Telescope: Aperture, Focal length and Resolving power

Telescope aperture

The telescope aperture is largely responsible for how much light the telescope can collect. The larger the aperture, the:

• larger is the resolution → more particulars / detail
• more brightly faint objects such as galaxies and nebulae are imaged at the same focal length
• But: the larger the aperture, the more sensitive the telescope is to air turbulence (seeing)

Since the telescope aperture is a circular area, increasing the aperture has a quadratic effect. If the aperture is doubled, the light gathering capacity is quadrupled.

Telescope focal length

The telescope focal length determines the magnification (visual in conjunction with an eyepiece) or the angle of view (when using a camera). An area of sky is projected onto the chip. The higher the focal length, the larger the objects appear. However, this also reduces the section that can be seen, which makes it more difficult to find objects and prevents the observation of large-area objects.

schematic illustration to visualize the focal length

With long focal lengths, aberrations are less significant because the light does not have to be refracted as much on the way from the telescope entrance to the focal point.

To get an impression of what commercially available telescopes with their different focal lengths can normally capture for a section of the sky, an illustrative image is shown below.

The following assumptions apply:

• The same camera chip is always used (APS-C format, 22.2x14.8 mm)
• No accessories like reducers or barlow lenses are used
• The following telescopes are compared:
  • Telephoto lens with 280 mm focal length
  • Refractor with 480 mm focal length
  • Newtonian telescope with 1000 mm focal length
  • Schmidt-Cassegrain-Telescope (SC) with 2000 mm focal length

Source: Rho Ophiuchi Komplex, Giuseppe Donatiello, CC0, via Wikimedia Commons (subsequently processed with rectangles for the field of view widths)

Resolving power of the telescope

The resolving power of a telescope is its ability to display two objects closely neighboring at an angular distance 'α' still separately. The resolving power depends on the wavelength of the light and the telescope aperture.
It can be calculated according to the Rayleigh criterion as follows (https://en.wikipedia.org/wiki/Angular_resolution#Explanation):

α – resolving power in ["]
λ – wavelength in [mm]
D – telescope aperture in [mm]

In this case Lambda is the wavelength of the light. Depending on the used filters, the appropriate wavelength can be used here for photography.

When viewing with an eyepiece, a distinction is made between photopic (day vision) and scotopic vision (night vision). During the day, the eye is most sensitive at a wavelength of 555 nm, at night it is 507 nm. (https://en.wikipedia.org/wiki/Luminous_efficiency_function)

The formula also shows the linear relationship between the telescope aperture and the resolving power. If the telescope aperture doubles, the value of the resolving power halves. The resolution is therefore better by a factor of 2 than before.