Light gathering and twight factor

Years ago an old friend who was the test pilot who sorted the P51 Mustang and who later had a great interest in hunting gave me a simple formula for assessing optimum x power for optics and scopes in particular. Apparently the human eye in perfect condition can discern light to a factor of 7. He told me that the formula to use was to divide the diameter of the objective lens of a scope by 7 to determine the optimum magnification power for best light gathering. For example with a scope like say a 3-12*42. Divide 42 by 7 = 7. Thus in dull light the greatest light definition for a human eye would be to wind the scope back to 7 power. As we age and visual acuity diminishes, we require more light entering our eye in order to see so an even lower magnification would be appropriate. In other words a fixed 4 * 32 scope will allow optimum light for a good eye. With a 3-12*56 scope the maximum light available would be 56/7 = 8 power.
With a 2-5 * 20 scope the optimum light sensitive magnification would be only about 3 power. A scope on 16 power would require a 112 mil objective lens to gain maximum usable light; so having your scope on high magnification in dull light may handicap you.
All that being said, I do not understand the european term "twilight factor" Can anybody clearly explain how this rating applies to scopes?

You have some of the right numbers, but not quite right - the "factor of 7" is most likely referring to the exit pupil of 7mm.

Dividing the objective diameter by 7 gives you the magnification figure which achieves maximum possible brightness. E.g. it won't get any brighter (as perceived by the human eye) in lowering the magnification, but it will get darker if you increase the magnification. As you get older, the maximum size of your pupil reduces, so going to even lower magnifications doesn't help.

I am skeptical of the practicality of the formula because the maximum diameter of the human pupil varies hugely, and it doesn't take any consideration into the quality of the glass and coatings, which is the main contributing factor for light transmission (as I understand it).

Additionally, I don't think there's any practical use for such a formula - you zoom out to find the target, and zoom in to whatever you feel comfortable with to shoot. No maths needed. Plenty of targets have been hit at 16 power without 112mm objective lenses.

Useful links:
Telescope Equations: Minimum Magnification
Scope Formulas

I hadn't heard of "twilight factor" before but it appears to be another useless formula for trying to quantify and compare low light performance:
Optics Myth 9 - "Twilight factor" is key to performance in dim light

The human eye has an upper limit of what light is can perceive. Thats what the factor of 7 is all about. In brief, its better to use scope on lower magnification to get the most from it in low light. Certainly it is true that high quality glass and lens coating will improve definition and low light capability, but not beyond or above what the eye is capable of absorbing.

The Europeans figured it out early on in hunting scope history the favourite scopes for twilight hunting are the 6x42 and the 8x56 both give a 7mm exit pupil
then the vari powers came along, it is still hard to beat the original two fixed power scopes for dim light,

Yep. My old 4*32 MX8 Leupold with tapered crosshairs was brilliant. I gave it to a young relly years ago. Regretted it ever since

A larger exit pupil gives more "eyebox" when shooting unorthodox postitions as you often do in the last of light or under artificial light. ie bigger objective and less mag.

Woody...they still are bud. my good Mrs bought me one off trademe that had just been back through loopy factory for refurb....... she is awesome wee scope for bush work,lives on my 7.62x39mm at the moment but might go back onto .308.
also own a 1.75-5 x20mm tasco and its light gathering is absolute crap on any power setting,its not even as bright as other scopes on sunlit days in open conditions.

also own a 1.75-5 x20mm tasco and its light gathering is absolute crap on any power setting,its not even as bright as other scopes on sunlit days in open conditions.[/QUOTE]

Yeah you get what you pay for specially with optics, My bush scope is an old Khales 2.5X that was abused by the boys in blue picked up for less than a new Bushnell or Tasco
it's crystal clear has better resolution than most scopes and never shifts zero, it may not be the best at twilight but I don't like being out after dark.

you are so right there...bought it on recomendation of sports shop owner as he didnt have anymore of the simply brilliant older nikko stirling 3x9x40mm gold crowns.Ive got one of those left and it has by far the best field of view of any of my scopes.....pity one of the big name brands dont duplicate it with thier reliability factor built in...it also works great at both ends of day and in spotlight...
if you happen to "trip" over any more of those kahles...drop me a line will ya???

The "twilight factor"was explained to me many years ago by a gunsmith and seems to make sense. Sometimes the twilight figure was expressed in the nomenclature of the scope. Example - remember the Pecar 4x scopes that were very popular in the 1960's/70's? They were designated 4x81 and obviously didn't have an 81mm objective. The figure of 81 is derived from the actual scope exit pupil of 9 which is then squared (9x9=81). The real objective diameter of the Pecar was 36mm (4x9=36).

Similarly, some lower end Japanese brands fixed 4x scopes were advertised as having a twilight figure of 100. These had a 40mm objective - thus 40 divided by 4 gives an exit pupil of 10 and 10 squared (10x10) is 100. You never saw higher grade fixed 4x scopes such as the European and U.S. brands have 40mm objectives as the human eye can't use an exit pupil of 10mm so the larger objective was unnecessary.

Its interesting theres no entry for "Twilight Factor" in Wikipedia.

Astronomics.com offers this definition:
Square Root of (allows for logarithmic sensitivity of an organic sensory system using Chemical reactions -your eye)

Square of objective lens diameter in mm ( area of front
lens determines number of photons collected )
×
magnification squared ( allows for concentration of those photons into a smaller area )

So this is the intensity of light (flux) reaching your eye.

As noted above, the maximum diameter of human pupils is about 7mm.

A wider exit pupil can be useful if you don't align your eye exactly eg Snap shooting or Left handed. But generally with a lower power scope there is little benefit in a huge objective lens. Once you get to 8X the exit pupil will usually be <7 mm.

So, are you better to have those photons concentrated into 3mm dia or is 6mm better ?

I believe it is often an advantage to use higher power eg 8x, rather than lower like 4x because the image is larger. Visual acuity is often a limiting factor in low light because the colour photoreceptor cells (cones) are small and close together, giving fine resolution but stop working in low light. The black and white receptors (rods) are more sensitive but further apart. So if its too dark to see colours-you need higher magnification.

I also believe designers optimise the image properties of their scopes for the middle of the magnification range (eg 6x for a 3-12× scope ).

Finally if you're over 60 you will have some cataracts and your low light vision will be greatly improved by having an operation ( in your shooting eye at least). This it quite expensive but so is a 56mm Nightforce on Kahles. Note that after a cataract up you will have no focussing ability so will likely need reading glasses and a parallax ( focus) adjustable scope.

other people in the above have been given correct explanation. This is my take:

The starting point is that human eyes can only have 7mm pupil, so anything more than 7mm is a waste. you are just carrying glass unnecessarily. there are some 4x50 scopes out there, for example.

Things get a little interesting then you have a variable power scope. with a given sized objective glass, obviously when you wind the power down you get more light to your eye. But again the most your eye can get 7mm, so if you have a 4-12x42, you will fine the scope get brighter as you move down power, but it should get no brighter past 6x power.

This does not mean, however, 6x power is the best. Arguably while you get more light you get less magnification, so you may well find, despite of it being brighter, it is harder for you to see your target, and you may well find 12x power gives you a better view, dimmer but clearer.

The math simply means that you get no gain by going below 6x power.

In real life people have different pupil sizes and as they age they lose the pupil size at different rate. Some people maintain 6.x mm even into their 60s, while others do not. So to have a practical value of this particular knowledge you really need to go out in twilight and play with your variable scope to find out what power works for you. If you are over mid-30s, your pupil may well have lost its best flexibility, you may well find yoruself seeing no brightness difference between 6x to 7.5x on a 42mm lens.

" you really need to go out in twilight and play with your variable scope to find out what power works for you. "

I guess there are two situations:

You are about to buy a new scope and want to work out how big you need the objective. All I can say is that bigger is better and 21st century is better than 20th. Go by reputation and practicality: do you want to carry a 50 or 56mm scope ? Can you mount it on your gun and will you need a raised cheekpiece ? My 2c is that I've seen a noticeable difference between 44, 50 and 56 mm in the 3-12 range. 50 and 56 are brighter than I can see with my naked eye so they are bright enough. It's not often you want to shoot something you can't see without optics. Of course if you can see it by eye but not through your scope you're onto a loser and that has happened to me often with a 2-7x32. Note that binoculars have twice the glass (sounds obvious) so my 8x32 binos are pretty much the same as my 3-12x50 scope and both are brighter than naked eye which is bright enough.

Then there is when you've got a scope and want to know quickly what power to turn it to for best visibility when shooting. As said, go out in the bush at a long distance and watch as the light fades, turning the power up and down for comparison. Look at something: "is it a log or is it a deer ?" Try something bright and something dark like a log inside the bush edge. If you've got a better optic to compare with, use that too. You will need to rest your gun solidly so there is no tremor. With my 3-12x50, I found I could see best at about 7x (later on I calculated out why ...) but it was true, taking into account size of image and brightness I could see the most detail at 7x. Other factors can affect your choice; in my case I've got a first focal plane unilluminated reticle which is pretty fine and hard to see below 4x and a lot easier to work with over 10x. If you have illumination, then flare may obscure the target at some powers, specially depending on the condition of your eyes. I you're spotlighting you will need wide field of view and for possums a low power helps to focus if they are very close. Some scopes have poor resolution in their upper range and whether its bright or big or not you can see better at lower power.