Focal ratio confusion

[Satchmo]

EDIT Just noticed this was the beginners section so just ignore if you're not yet competant with the relationship between magnification , exit pupil and aperture !

This discussion ties in with an add I saw the other day for Vixen 2X 40mm mini binoculars and prompts my usual rant about `unity brightness' and the human eye

Provided you fill the fully dilated pupil you cannot make an extended object brighter by increasing the size of the telescope . You can only make it appear larger by increasing the aperture . The increase in visibility of faint galaxies comes about because the resolution of the eye drops to one or two degrees at low light levels and filling the pupil with an(increasingly larger telescope only makes its apparent size larger and thus becomes visible . There is also an amplifying effect where the rods in the eye can be brought into play with averted vision though !

Its called `unity brightness' and its a concept that helps to understand human interaction with telescopes , where the eyes are not CCD chips , but limited by that physical bottle-neck of the iris.

A simple demonstration with our Vixen 2 X 40mm binoculars . At 2 X magnification ( and 7mm pupil ) we can't see more than 14mm of the 40mmm aperture due to the vignetting of the Iris. We have doubled the effective aperture over the unaided eye and are using 4 X the surface area of optic over the 7mm pupil but we have also increased the size of the image on the retina by 2X and hence reduced the surface brightness of the image by a factor of 4X .

The net result is a zero increase by unit area of light on the retina , and this relationship continues on adfinitum as we increase aperture .
tThis is just pure maths but the visibility of faint objects is further enhanced in the eye by the physiological nature of rods and cones . Theres good treatment of this subject and unity brightness in this article from Page 35 link below on extended objects ..avoid the maths if you are squeamish and stick to the text .

Point sources behave differently but in bad seeing even stars can start to behave like extended objects !

https://books.google.com.au/books?id...pe%20s&f=false

[N1 (Mirko)]

I expect the 40mm aperture of the Vixens is the most efficient way to achieve their TFOV, i.e. the purpose of the large aperture here is a wide angle, as opposed to light gathering?

[Satchmo]

Originally Posted by N1

I expect the 40mm aperture of the Vixens is the most efficient way to achieve their TFOV, i.e. the purpose of the large aperture here is a wide angle, as opposed to light gathering?

Hi Mirko The 2X magnification should give a large true field of view. The 40mm aperture is just there probably to make the binoculars large enough to hold as the most aperture you will be able to utilise with young eyes is about 14mm which wouldn't look so impressive in the advertising and they would be tiny . The relationship between magnification and aperture is magnification X exit pupil = aperture and pupil maybe open to 7mm when you are young.

[Finite (John)]

Does the brain combine the images from both eyes, so is making use of 7 mm of pupil x 2, is that how you achieved the 14mm of the 40mm available through the binos?

[N1 (Mirko)]

Originally Posted by Satchmo

Hi Mirko The 2X magnification should give a large true field of view. The 40mm aperture is just there probably to make the binoculars large enough to hold as the most aperture you will be able to utilise with young eyes is about 14mm which wouldn't look so impressive in the advertising and they would be tiny . The relationship between magnification and aperture is magnification X exit pupil = aperture and pupil maybe open to 7mm when you are young.

Hi Mark that would be quite neat actually. Imagine a pair of 2x14s for your shirt pocket
Would they need more strongly curved lenses perhaps?

John, I think what Mark means is that with an iris opening of 7mm, you'd be using 14mm of the 40mm, because aperture divided by power equals exit pupil. I won't comment on the bino effects because I don't know a lot about binoviewing. Steve et al. might be able to help.

[janoskiss (Steve H)]

@N1 It sounds like you and I were on the same page all along as far as the cold hard facts of the matter are concerned --- saying much the same thing but in conflicting sounding ways, and we may have somewhat different personal preferences too (which is a good thing; visual astronomy is all in the eye of the beholder after all).

I like Mark's analysis why they had to make it 2x40 instead of 2x14 - advertising and marketing! I could definitely go for a well made 2x14 or 3x20.

[janoskiss (Steve H)]

Originally Posted by Finite

Does the brain combine the images from both eyes, so is making use of 7 mm of pupil x 2, is that how you achieved the 14mm of the 40mm available through the binos?

No, it's about the 2x magnification. Aperture / Magnification = Exit Pupil. In this case 14mm/2 = 7mm. Two eyes or one don't matter as far as exit pupil goes. If you wanted say 5x magnification, then the largest useful aperture would be 5x7mm = 35mm.

[Finite (John)]

Ta, as you can see i'm no professor.

[janoskiss (Steve H)]

The human eye pupil size can be such a bottleneck that some people even resort to performance enhancing drugs for visual astronomy: http://www.aapos.org/terms/conditions/43

You will look pretty scary though to your fellow stargazers at the 5am tea break.

[Satchmo]

I've got to do those drops with a 30mm 100 degree apparent field eyepiece and a 24" F3.5 at least once in my life

[N1 (Mirko)]

Steve, yes that has been my impression also. Visual sure is a subjective beast. Re destruction of galaxy, I'm sure it's nothing a beer or two couldn't fix/prevent

[Finite (John)]

Update to something I posted earlier, - seen a galaxy now - Thanks to Dave Brock👌