8 minute lesson · Astronomy · Original foundation material
Before you start: Area of a circle; Ratios; Focal length.
A telescope collects light and helps separate fine detail. Magnification is only one part of the story. Learn to distinguish aperture, focal length, magnification and resolution before using a formula.
Aperture controls collecting area
The aperture D is the diameter of the main light-collecting opening. For an unobstructed circular opening, area = πD²/4. At the same incoming light intensity, equal transmission and equal exposure time, the collected energy scales as D².
Doubling the aperture therefore collects four times as much energy. This statement concerns total collected light; it does not mean every extended object's image becomes four times brighter at every magnification.
Magnification and focal ratio
For a simple visual telescope focused at infinity, the magnitude of angular magnification is M = fo/fe. Here fo is the objective's focal length and fe is the eyepiece's focal length. Use the same units for both.
The focal ratio is fo/D. An objective with focal length 800 mm and aperture 100 mm is f/8. A shorter-focal-length eyepiece increases magnification, but it cannot restore detail that the instrument has failed to resolve.
Resolution has a limit
For an ideal circular aperture, the Rayleigh angular resolution is approximately 1.22λ/D radians. A smaller angle means finer resolvable detail. At fixed wavelength λ, doubling D halves this angle. Real observations can also be limited by atmospheric turbulence, focus and optical quality.
A worked example
A visual telescope focused at infinity has a 120 mm aperture, a 960 mm objective focal length and a 24 mm eyepiece focal length. Find the magnitude of its angular magnification and its focal ratio.
- All three lengths are in millimetres, so the ratios are ready to use.
- Magnification is fo/fe = 960/24 = 40.
- Focal ratio is fo/D = 960/120 = 8.
- State the two results separately: 40× magnification and an f/8 objective.
40× magnification; f/8
Check your understanding
Replace the 24 mm eyepiece in the example with a 12 mm eyepiece. What changes?
Show the explanation
Magnification becomes 960/12 = 80×. The aperture, collecting area and f/8 focal ratio remain the same.