Why does the recommended focal ratio for an achromatic refractor rise with aperture?

Question

talking about achromatic refractors only and data from this sheet:
http://www.gaherty.ca/rogers/achrefract.htm

I already know about chromatic aberration!!!!!!
I ask why it is more pronounced with larger refractors

Arkalius-see my previous questions and realize you're not my brain-lord!Second-even if you are right then nothing is on your way to give me some more info!-I am going to report you for calling me rude when I am not!
Guys i believe Adolph is right - even though Barlow doesn't change focal ration of the objective (it changes the eyepiece's) it filters the rays with steeper angle thus the image becomes less panoram, less bright and why not less aberrated?

Answer 1

Stated in a very simplified way, when we talk about focus, it is almost always discussed as a point where light rays come together.
But that is not true. There is really a "Zone" of focus. This zone has a certain depth.If all the light focuses within that zone, there will be no aberration.
The reason chromatic aberration disappears with longer focal lengths is because the light rays ( some books call them pencils) come to focus at a shallower angle as the F/ratio increases. This enlarges the zone of focus. If the zone of focus becomes long enough so that all light frequencies come to focus within the zone, chromatic aberration disappears.
A three inch Refractor needs about F/15 to F/16 (there are two formulas out there, depends on whom you believe) while my 6" Refractor needs about F/18 to F/20 to eliminate the aberrations.
This was the original purpose for the Barlow Lens, NOT additional magnification as most people think today.
It allowed large refractors to have optical tubes of reasonable length and still be able to eliminate most of the chromatic aberration.
With the Televue 2.5X powermate, my 6" F/8 Refractor becomes a 6" F/20 instrument and there is indeed no false colour that i can detect, although I am sure there is some small residual aberration present, but I can't see it.
No $10,000.- Apochromat needed.
BTW, An Apochromat is NOT colour free! An Apochromat focuses three colours instead of the Achromats two!
Anyway, hope that helps.

Adolph

Answer 2

Achromatic refractors suffer from chromatic aberration. This aberattion is reduced by having a slower focal ratio. Larger apertures will feature more prominent aberrations so slower focal ratios are recommended for them.

Edit: "I already know about chromatic aberration!!!!!!
I ask why it is more pronounced with larger refractors"

To be fair, no you didn't. You asked why it is recommended to have a higher focal ratio, and made no mention of knowing about chromatic aberration. I answered the question you asked, there is no need to be rude to me for not knowing what you really meant to ask.

Chromatic aberration increases as focal ratio decreases AND aperture increases. The lenses are larger on a larger aperture so there is more light to split into colors.

Answer 3

No time to go into the math but briefly, the diameter of the color blur is proportional to aperture and the diameter of the airy disc (star image) is proportional to focal ratio. So to keep the chromatic aberration the same proportion of the telescope's resolution, you have to increase focal ratio in proportion to aperture.

Answer 4

Thanks for reading my article!

The detailed mathematical argument is in J. B. Sidgwick: Amateur Astronomer's Handbook (Faber 1955, but there are newer editions, including a Dover reprint). It's on pages 87 to 96 in the first edition, at the end of the chapter on aberrations, so too long to try to summarize here. A wonderful book, by the way!