Formula & Calculator
Telescope Focal Ratio (f-number)
The ratio of a telescope's focal length to its aperture diameter, determining image brightness and field characteristics.
Interpretation
f/# = f / D. Focal ratio of a telescope, ratio of focal length to aperture. Affects exposure time and field of view. Used in astrophotography.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| f/# | Focal ratio | |
| f | Focal length | mm |
| D | Aperture diameter | mm |
What it means
The focal ratio (f‑number or f/stop) is the ratio of a telescope’s focal length (f) to its aperture diameter (D). A lower f/# means a “faster” optical system, resulting in shorter exposure times for astrophotography, but often with a smaller field of view. It influences the brightness of the image and the field of view. It is used in photography and astronomy to determine exposure settings and to select instruments for specific imaging targets. Understanding this helps photographers and astronomers choose appropriate setups for their applications.
Worked example
Telescope Focal Ratio – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| f (mm) | 1000 |
| D (mm) | 100 |
| Parameter | Value |
|---|---|
| f | 600 |
| D | 80 |
Common mistakes
- Focal ratio (f/#): f / D – where f is focal length, D is aperture (both in same units).
- ‘f‑number’: A smaller number means a faster telescope (shorter exposure).
- Units: f and D must be in the same unit (e.g., mm) – ratio is dimensionless.
- Common values: f/4‑f/10 for amateur telescopes.
- Focal ratio: Affects field of view and image brightness (for extended objects).
Applications
The focal ratio (f‑number), f/# = f / D, is the ratio of the telescope's focal length (f) to its aperture diameter (D). This determines the speed of the optical system – lower f/# means faster and wider field of view, suitable for astrophotography. Astrophotographers choose telescopes with low f/# for capturing faint nebulae and galaxies. It also affects image brightness and exposure time. By understanding f‑number, observers can select appropriate instruments for visual and photographic applications. This parameter is also used in camera lenses. Knowing the focal ratio helps in planning exposures and in comparing optical systems.
- Astrophotography – selecting telescope for wide‑field or deep‑sky imaging
- Estimating exposure times for astronomical targets
- Comparison of optical systems for various applications
- Design of camera lenses and telephoto optics
- Educational understanding of optical system performance
Frequently Asked Questions
f/# = f / D, where f is the focal length and D is the aperture diameter. It is a measure of the telescope's light‑gathering speed; a smaller f‑number means a faster optical system (brighter images for extended objects).
For extended objects (e.g., nebulae, galaxies), the image brightness is proportional to 1/(f/#)². A telescope with f/5 is (10/5)² = 4 times brighter than an f/10 system of the same aperture, for extended objects.
For a given eyepiece, a shorter focal length (lower f/#) gives a larger true field of view, because the focal length is shorter. This is why fast telescopes are preferred for wide‑field astrophotography.
- Fast (e.g., f/4): brighter images, wider field, but more optical aberrations (coma, astigmatism) and more difficult to focus.
- Slow (e.g., f/10): better correction, easier to focus, but dimmer and narrower field.
For extended objects, exposure time scales with the square of the f‑ratio. For example, switching from f/8 to f/4 reduces exposure time by a factor of 4 for the same brightness.
f/# = 2000 / 200 = 10. So it is an f/10 system.
A Barlow lens multiplies the effective focal length, thus increasing the f‑ratio. For example, a 2× Barlow on an f/5 telescope makes it f/10. This increases magnification but decreases brightness.
Refractors: f/6 to f/9 (slow to moderate). Reflectors (Newtonians): f/4 to f/8. Schmidt‑Cassegrains: f/10. Fast astrographs: f/2 to f/5.
In photography, depth of field is affected by f‑number. However, in telescope optics, depth of field is usually not a concern because objects are at infinity. However, for close focus (e.g., lunar), depth of field is small at low f/#.
Not necessarily. While it gives faster exposure, it also requires better optical quality and may suffer from vignetting and aberrations. Also, for point sources (stars), brightness depends only on aperture, not f‑ratio.