How to calculate a
telescope's
magnifying power and
f/ratio
Magnification:
To change the magnifying power
of any telescope simply change the eyepiece. Different
eyepieces have different focal lengths, the shorter the
focal length of an eyepiece, the higher the
magnification. However, the eyepiece is not set to a
given magnifying power, because its magnifying abilities
are dependent upon the objective lens. So an eyepiece
that provides a 16X magnifying power on one telescope,
may provide a 50X magnifying power on a different
telescope; it's all dependent upon the focal length of
the given telescope's objective lens or mirror.
To calculate the magnifying power of
any telescope you simply divide the focal length of
the objective lens or mirror by the focal length of the
eyepiece. Remember to use the same measuring units,
eyepieces are generally sold by their focal length in
millimeters, telescopes are often sold by their focal
lengths in centimeters or inches. Don't forget to convert
first!
Magnification=Focal length of the
Objective/Focal length of the Eyepiece
OR
M = Objective f.l./Eyepiece
f.l.

A Magnifying
Challenge!
Let's say we have three telescopes.
One is a Catadioptric
type of telescope with a primary mirror that is 8" in
diameter and has a focal length of 2000 mm. The second
scope is a Refracting
telescope that has a primary lens that is 60 mm in
diameter and has a focal length of 800 mm. The third
telescope is a Reflecting
telescope that has a primary mirror that is 4" in
diameter and has a focal length of 450 mm.
We have three eyepieces too. Each has
a different focal length. The lengths are: 8 mm, 12 mm,
26 mm.
Can you calculate the various
magnifying powers of the three telescopes described and
how they will vary depending on which eyepiece you
use?
for
answers...

8 mm f.l.
eyepiece

12 mm f.l.
eyepiece

26 mm f.l.
eyepiece

Catadioptric 2000 mm f.l.
8" diameter

?

?

?

Refractor
800 mm f.l.
60 mm diameter

?

?

?

Reflector
450 mm f.l.
4" diameter

?

?

?

Remember: M = Objective f.l./Eyepiece f.l.

f/Ratio:
The f/ratio of a telescope is
determined by dividing the focal length of the primary
lens or mirror by the aperture (the diameter of that same
lens or mirror). This number tells us several important
things about a telescope. For example, the lower the
f/ratio the faster the telescope is said to be; that
basically means that it provides a brighter image than a
similar sized telescope with a higher f/ratio. Yet,
remember that there is always a tradeoff, by getting
brighter images you loose some magnifying power.
Telescopes with low f/ratios give widefield images with
bright star fields, they are good for viewing star
clusters and faint nebulae. Telescopes with high f/ratios
aren't quite as bright, but yield higher magnifications
with narrower fields of view. They are ideal for planet
viewing and splitting binary stars.
f/6 and lower would be
considered fast, ideal for viewing faint nebulosity and
wide field objects.
f7 to f/10 would be midrange.
The compromise range, telescopes with f/ratios in this
range do fairly good at both ends.
f/11 and up would be considered
slow, but ideal for planetary work or studying
binaries.
Again, when calculating f/ratios,
remember to use the same units of measure. Don't
divide centimeters by inches!
f/ratio = focal length /
aperture
*AN IMPORTANT POINT*
Remember that using f/ratios to compare two
telescopes works best when things are equal otherwise. A
10 inch f/11 may very well give you much brighter images
than a 4 inch f/6 because it has more light gathering
abilities with it's greater aperture. A safer comparison
would be comparing two telescopes of the same aperture,
but with different f/ratios.

1. Which would provide a brighter image an 8 inch f/10
or an 8 inch f/6?
 2. Which would provide more
magnification, a 6 inch f/8 or a 6 inch f/5?
 3. Which would provide a wider
field of view a 4 inch f/6 or a 4 inch
f/4?
Answers

f/ratio
Challenge!
Using the same three telescopes as
above, calculate their f/ratios. Which one would be best
for planetary studies? For studying nebulae?
Telescope

Focal
Length

Aperture

f/ratio

Catadioptric

2000 mm

8 inches or 203
mm

?

Refractor

800 mm

60 mm

?

Reflector

450 mm

4 inches or 102
mm

?


Don't Scroll Any
Further Down
Unless You Want To See The Answers!

Answers!
Magnification Table
Solution:
back...

8 mm f.l. eyepiece

12 mm f.l. eyepiece

26 mm f.l. eyepiece

Catadioptric
2000 mm f.l.
8" diameter

250 X

167 X

77 X

Refractor
800 mm f.l.
60 mm diameter

100 X

67 X

30 X

Reflector
450 mm f.l.
4" diameter

56 X

37 X

17 X

f/ratio
questions:
 1. An 8 inch f/6 would provide
brighter images than an 8 inch f/10.
 2. A 6 inch f/8 would provide
greater magnification than a 6 inch f/5.
 3. A 4 inch f/4 would provide a
wider field of view than a 4 inch f/6.
back
to f/ratio questions
f/ratio Table
Solution:
Telescope

Focal
Length

Aperture

f/ratio

Catadioptric

2000 mm

8 inches or 203
mm

f/9.8

Refractor

800 mm

60 mm

f/13.3

Reflector

450 mm

4 inches or 102
mm

f/4.4

back to
f/ratio table


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