How are Focal Length, Magnification and FOV Related?

To know how your scope will perform and what objects it is best suited to view, you’ll need to know a few things. Start with your telescope’s focal length and objective diameter, plus the AFOV for each eyepiece.

• Example Equipment Specs To simplify the math, I’ll select two common scopes to use in our examples:
  • Scope 1 = 100mm objective with a 500mm focal length
  • Scope 2 = 200mm objective with a 2000mm focal length
    
• Focal Length (ƒ) is the distance from the objective (primary) lens or mirror to the point of focus at the eyepiece.
  
• Objective Diameter (D) is simple the diameter of the primary mirror or lens.
  
• Focal Ratio is the focal length divided by the diameter (ƒ / D) and is usually expressed as f/#.
  • Note that you must use the same units (mm or inches).
  • Scope 1: 500/100=f/5
  • Scope 2: 2000/200=f/10

• Magnification (Mag) of a scope is ƒ / eyepiece ƒ (focal length / eyepiece focal length)
  • Each telescope focal length has a magnification range that is modified by the eyepieces you use.
  • Common eyepieces range from 10mm to 25mm focal lengths.
  • You can modify the magnification range with Barlow lenses (increasing focal length) or focal reducers (decreasing focal length).
  • Scope 1 w/25mm Plossl eyepiece: 500/25=20x
  • Scope 1 w/25mm Plossl and a .5x focal reducer: (500/25)/2=10x
  • Scope 1 w/10mm Plossl eyepiece: 500/10=50x
  • Scope 1 w/10mm Plossl and a 2x Barlow: 2*(500/10)=100x
  • Scope 2 w/25mm Plossl eyepiece: 2000/25=80x
  • Scope 2 w/10mm Plossl eyepiece: 2000/10=200x
    
• Apparent Field of View (AFOV) is a design specification for each eyepiece design.
  • The manufacturer should list the AFOV of each eyepiece on their web site, sales material, or manuals.
  • Plossl eyepieces commonly have an AFOV of 50°.
  • High end eyepieces can expand the AFOV to 70° or more.
    
• Field of View (FOV) for a telescope is AFOV eyepiece / Mag
  • Scope 1 w/25mm Plossl eyepiece (20x): 50/20=2.5°
  • Scope 1 w/10mm Plossl eyepiece: (50x): 50/50=1°
  • Scope 2 w/25mm Plossl eyepiece: (80x): 50/80=0.625°
  • Scope 2 w/10mm Plossl eyepiece: (200x): 50/200=0.25°
  • Scope 1 w/10mm Plossl and Scope 2 with a 40mm Plossl both reach 50x, with a 1° FOV.
    
• Power Per Inch (PPI) for a telescope is Mag / D
  • Use inches for the diameter (25mm roughly equals 1 inch)
  • PPI of 30-50 is a good guide for maximum magnification on your telescope.
  • Scope 1 w/10mm: 50/4= 12.5
  • Scope 1 w/10mm and Barlow: 100/4= 25
  • Scope 1 w/10mm and 4x Barlow: 200/4= 50
  • Scope 2 w/10mm: 200/8=25
  • Scope 2 w/10mm and Barlow: 400/8=50

So now we’ll take a look at what these numbers mean and how they effect your view of the sky.

Focal Ratios

Focal ratios in common use by amateur astronomers range from f/4 to f/10. Wider and narrower telescopes exist, but are less common. Amateur astronomers tend to categorize ratios into wide, medium, and narrow views. Imagine wide angle views by touching your thumb to forefinger so you have a circle and place it around your eye. A narrow field of view would be looking through a paper towel roll or even a drinking straw.

• f/2 – Extreme wide angle view
  • Extremely short focal length that is difficult to align and focus because the light cone is so steep.
  • Fairly rare in amateur telescopes, though very large research scopes can be in this range.
• f/4-f/5 – Wide angle view
  • Common in small refractors, binoculars, and some reflectors.
    • Refractors are susceptible to chromatic aberration at this short focal length.
    • Reflectors are susceptible to coma aberration at short focal lengths.
  • 3-5″ Scopes: f/4-f/5 is ideal for wide objects like open clusters, large galaxies, and wandering through the Milky Way.
  • 6-10″ Scopes: f/4-f5 gives wide views with great light gathering, but the scope will lack magnification to show the planets well. Uncommon in commercial scopes.
  • 12″-16″: These larger scopes often run f/4 or f/5 because the scope’s longer focal length causes a narrow view.
  • 18″ and up: The largest scopes run f/5 or wider almost exclusively to avoid “drinking straw” views and huge ladders.
• f/6 – Medium view
  • Telescopes up to 8″: f/6 is a good all-around performer that lets you view both wide and narrow objects. A few high end refractors come in at f/7.
  • 10-15″ telescopes: f/6 is starting to get a bit narrow, without the higher magnification found at f/8 and higher. Most scopes this size are f/5 or wider.
  • In larger telescopes, f/6 is uncommon thanks to the narrow view.
• f/8-10 – Narrow view
  • 3″-4″ telescopes: Small refractors can come in at f/10
  • Telescopes 5″ and up: f/9 or f/10 is common for Schmidt-Cassegrain (SCT) and other compound telescopes.
  • Maksutov-Cassegrain (Mak-Cass) telescopes come in f/10 to f/12.

Practical Examples:

If you’re still not sure how this works, perhaps these charts will help explain how a telescope’s focal length, focal ratio, and magnification interact. Each chart keeps one of the three specifications the same while changing the others.

• Green on the chart is the primary unchanging factor.
• Red is what I’m changing.
• Yellow is the results.
• Black is unchanging, but unimportant

Eyepiece Parameters

Since your telescope’s objective diameter and focal length are fixed, eyepieces are the one thing you can easily change in this equation. Note that shorter eyepieces give you higher magnification and narrower FOV.

What happens when you change the AFOV of an eyepiece?

This is the reason why many amateur astronomers pay big bucks for high end eyepieces with a 60+ degree field of view, especially for telescopes with long focal lengths and high natural magnification. Since 2″ eyepieces are easier to design with a wider view, they are a popular option.

Telescope Parameters

Next let’s tinker with scope parameters and see how that changes our magnification and FOV. First up, let’s look at increasing diameter to a whopping 27″ telescope:

Now let’s flip this on its ear and increase the scope’s focal length while keeping a 100mm objective and a 20mm Plossl eyepiece. Note how the Magnification and FOV change as the focal length gets longer:

Telescopes with longer focal lengths will have higher magnification and narrower field of view. Longer focal lengths are better suited to smaller objects while shorter ones are better for wide views.

Power Per Inch

Note how Power Per Inch changes with decreasing eyepiece focal length. Judging if a scope and eyepiece combination would work in Earth’s soupy atmosphere is the primary function of PPI.

How does Power Per Inch change with increasing telescope focal length?

Object Dimensions For Reference:

• M31 Andromeda Galaxy is 3° x 1°
• M24 Small Sagittarius Star Cloud is 2° x 1°
• M45 Pleiades open Cluster is 2°
• Orion Nebula and Ptolemy’s cluster are 1°
• M57 Ring Nebula is 0.6°
• The Moon and Sun are 1/2°
• Hercules and M4 Globular Clusters are 1/3°
• Crab Nebula and Omega Nebula are 1/10°
• Galaxies range from 3° down to 1/10° or less.

More Reading

• Simple Formulas for the Telescope Owner – Sky & Telescope – Sky & Telescope (skyandtelescope.org)
• f-number – Wikipedia
• Focal Length & Ratio Calculator astronomy.tools