Telescopes are usually sold with the size of the aperture prominently advertised. This number is usually not given for camera lenses though, where the focal length and focal ratio are featured.
The three parameters of interest for camera lenses and telescopes are their aperture, focal length and focal ratio.
Aperture - the size of the opening that collects light. The larger the aperture, the more light is collected.
Focal Length - the distance behind the objective lens or mirror where the image is formed. More focal length gives more magnification.
Focal Ratio - the ratio between the aperture and focal length. A "faster" focal ratio (shorter focal length for a given aperture) concentrates more light into a given area at the focal plane allowing shorter relative exposures than a "slower" focal ratio (longer focal length for a given aperture).
You can also think of it like this: for the same focal length, a larger aperture means a "faster" focal ratio and more light collected at the focal plane, allowing shorter exposures.
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Formula 1 Inches to Millimeters
mm = I * 25.4
Where:
- mm = millimeters
- I = inches
- 25.4 = the number of millimeters in an inch
Example: How many millimeters of aperture are there in a lens that has a diameter of 5 inches?
mm = I * 25.4
mm = 5 x 25.4
127 millimeters
5 inches equals 127 millimeters.
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Formula 2 Focal Ratio or F/number
F# = FL / A
Where:
- F# = F/number or Focal Ratio
- FL = Focal Length
- A = Aperture
Example: What is the focal ratio of a telescope that has a focal length of 1040mm and an aperture of 130mm?
F# = FL / A
F# = 1040 / 130
F# = 8
A telescope that has a focal length of 1040mm and an aperture of 130mm has an F/number of F/8.
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Formula 3 Focal Length
FL = A * F#
Where:
- FL = Focal Length
- A = Aperture
- F# = Focal Ratio or F/number
Example: How many millimeters of focal length are there in a lens that has a diameter of 130mm and an f/number of 8?
FL = A * F#
FL = 130 x 8
1,040 millimeters
A lens that has a diameter of 130mm and an f/number of f/8 has a focal length of 1,040 millimeters.
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Formula 4 Aperture
A = FL / F#
Where:
- A = Aperture
- FL = Focal Length
- F# = F/number or Focal Ratio
Example: How many millimeters of aperture are there in a lens that has a focal length of 600mm and an f/number of f/6?
A = FL / F#
A = 600 / 6
100 millimeters
A lens that has a focal length of 600mm and an f/number of f/6 has an aperture of 100 millimeters.
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| Various Camera Lenses |
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| Focal Length |
F/Ratio |
Aperture |
| 300mm |
f/2.8 |
107mm |
| 200mm |
f/2.8 |
71.4mm |
| 100mm |
f/2.8 |
35.7mm |
| 85mm |
f/2.8 |
30.7mm |
| 50mm |
f/2.8 |
17.8mm |
| 35mm |
f/2.8 |
12.5mm |
| 24mm |
f/2.8 |
8.5mm |
| 20mm |
f/2.8 |
7.1mm |
| 15mm |
f/2.8 |
5.3mm |
Note that with camera lenses, as you stop them down to smaller f/stops, you increase the f/ratio and the aperture is reduced.
| Various Apertures, Same Lens |
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| Focal Length |
F/Ratio |
Aperture |
| 300mm |
f/2.8 |
107mm |
| 300mm |
f/4 |
75mm |
| 300mm |
f/5.6 |
53.4mm |
| 300mm |
f/8 |
37.5mm |
| 300mm |
f/11 |
27.3mm |
| 300mm |
f/16 |
18.7mm |
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