Jim's Corner Blog

Common Telescope Formulas

For many amateur astronomers, these are common place telescope formulas that we learned early in our astronomy careers.

But to many, some of these formulas are unfamiliar, need to be looked up in a book, or are listed under the category of “How do you figure that out?”.

Telescope Magnification, or What power am I using?

The most common question when someone looks through a telescope.

M = focal length of telescope/ focal length of eyepiece

where the focal lengths of both telescope and eyepiece are in the same units.

M = f.l. telescope in mm/ f.l. Eyepiece in mm


M = f.l.telescope in inches/ f.l. in inches

Exit Pupil, or Am I seeing all the light?

A young person’s pupil can open to 7mm in dark conditions. Older eyes aren’t so night friendly, with pupils opening to 5.0mm to 5.5mm. So a eyepiece-telescope combination that yields an exit pupil of 8mm means you’ve wasted your money on equipment because the extra light is unseen and wasted.

Exit Pupil = D/M


D = the diameter of the telescope’s objective lens or primary mirror in millimeters

M = magnification = focal length of telescope/focal length of eyepiece

or Exit Pupil = F/f


F = the focal length of the eyepiece in millimeters

f= the telescope’s focal ratio ( the f-number)

True Field of View, or If my eyepiece has an apparent field-of-view, what is my real field?

If you can get 4° or 5° or more of True Field at low power with your telescope, you probably don’t need you finderscope anymore. Just a low power, wide field eyepiece. And the advantage is using a much larger aperture of the main telescope instead of a smaller aperture finderscope.

True Field = AFOV/M


AFOV = the apparent field of view of the eyepiece in degrees

M = magnification

Focal Ratio, or Why is my telescope so long or short?

A focal ratio of f/12 or more means easily attainable high power but a limited field-of-view. A focal ration of f/7 or even the shorter f/5 or less means low power wide field-of-view.

Focal Ratio = f.l./D


f.l. = focal length of the telescope

D = diameter of the telescope objective

Dawes Limit or Resolving Power, or What’s the smallest thing that I can see?

A double star or lunar observer is interested in this figure to determine the resolving limits of their telescope.

Estimate Resolving Power = 4.56/D in inches


Estimate Resolving Power = 116/D in mm


D = diameter of the telescope objective

Estimating Residual false color in Achromatic Telescopes, or Do I really need to spend $$$ to get a refractor that don’t show secondary color?

FromTelescope Optics: Evaluation and Design, by Harrie Rutten and Martin van Venrooij:

focal length >0.122D


D = diameter of the telescope objective in mm

If the focal length of an achromatic refractor is equal to or greater than this calculation, the residual chromatic aberration will not be a factor.

Jim's Corner Blog

The Best Worst Telescope: The Crossley

The historic Crossley reflector has been described as “the worst best telescope”. Its history dates back to 1879 where it was located in the backyard of Andrew Ainslie Common’s home in the Ealing district of west London, England. Common was an English amateur astronomer, who perhaps like many of amateur astronomers, suffered from a severe case of aperture fever.

For many years, Common used an 18 inch Newtonian reflector mounted in a shed built in his backyard in Ealing. Eventually, aperture fever took over and he commissioned the building of a 36 inch reflector of his own design and implementation, also installed in his backyard in Ealing, England. The optics of this telescope were outstanding, however the mechanical design showed a lack of engineering skill by Common. The primary mirror was mounted ahead of the vertical axis which caused a balance issue with the telescope, necessitating the use of counterweights. Strangely, Common used a polar axis design that used liquid mercury in its bearing mechanism, causing a mechanical and now recognized environmental issue. Mechanically, the telescope was awful. But Commons was able to perfect astrophotography techniques with this telescope.

The telescope was sold to British politician Edward Crossley in 1886, who operated the telescope until 1895. Crossley built a new dome enclosure to protect the telescope and observers from the harsh Halifax, England weather. But this climate was far from ideal for observation.

After about 10 years, Crossley donated both telescope and dome to Lick Observatory, where it was put into operation in 1896. Lick Observatory director James Keeler had the Crossley re-engineered mechanically by replacing the original mercury bearing mount with a conventional equatorial cross-axis mount. Director Keeler then put the Crossley to good use by producing early astro-photographs of “nebulae”, those fuzzy-looking areas in the night sky, not knowing that the future 100 inch Hooker telescope at Mt. Wilson would be used to discover many “nebulae” that were actually galaxies.

An example of the discoveries by the Crossley is Arp 148 was discovered by American astronomer Nicholas U. Mayall of the Lick Observatory, using the Crossley reflector. Arp 148, nicknamed “Mayall’s object” and is located in the constellation of Ursa Major, the Great Bear, approximately 500 million light-years away. Arp 148 is the aftermath of an encounter between two galaxies, resulting in a ring-shaped galaxy and a long-tailed companion. The collision between the two parent galaxies produced a shockwave effect that first drew matter into the centre and then caused it to propagate outwards in a ring. The elongated companion perpendicular to the ring suggests that Arp 148 is a unique snapshot of an ongoing collision. Infrared observations reveal a strong obscuration region that appears as a dark dust lane across the nucleus in optical light.


Arp 148 (NASA, ESA, the Hubble Heritage Team (STScI/AURA)-ESA/Hubble Collaboration and A. Evans (University of Virginia, Charlottesville/NRAO/Stony Brook University), K. Noll (STScI), and J. Westphal (Caltech)