Looking at scopes in a gun shop is about useless in determining how they will work in the field. Why can’t I find a simple set of equations to calculate how they will perform. Does anyone know how to calculate performance based on available numbers or a site that explains it? We do this kind of stuff for rifles all the time. Why are scopes so unscientific?

makeminestainless, that is a great question! I think a guy who posts here as Rick 0311 has a lot of technical knowledge of optics, hopefully he and others will enlighten us.

regards--Don

makeminestainless,

Scopes are actually far more “scientific†than rifles are...but it is impossible to create a meaningful formula that includes the greatest of all variables...the guy looking through it.

Even with rifles, we can calculate the theoretical amount of recoil produced with a certain load in a certain rifle, but that recoil may be perceived (felt) much different by me than it is to you.

“Relative Brightness†is a numerical value equal to the diameter of the exit pupil squared. Higher numbers are supposedly better and “brighter.â€

Exit pupil diameter= Objective lens diameter (in mm’s) divided by the magnification of the scope.

Example: A 40mm objective lens on a 10x scope will, theoretically, have an exit pupil of 4mm in diameter and a “relative brightness†factor of 16 (4 squared). The same size objective lens at 4x magnification would have a relative brightness factor of 100.

All of this sounds really cool, but it leaves out the most important factor of all...Your individual eyes, and the fact that the average adult pupil dilates to a maximum diameter of about 7mm (at night) and in normal daylight that size will go down to about 3mm or less.

IMO, the only practical way to judge the “brightness†of a scope is to actually look through it yourself in different lighting conditions. Scopes with better resolving power and better glass can oftentimes “appear†brighter than another scope even though the other scope might have a slightly higher brightness factor using the math.

Now if you think all this has confused you, go look at scopes with huge variable magnification ranges!

Bottom line...trust your own eyes not math formulas.

If all lenses and coatings were equal,the calculations would work.However,since lenses and coatings vary so much,a scope that should be brighter according to the calculations,may not actually be as bright.For example 3x9x40 with great lenses and coatings may be as bright or even brighter brighter than a 3x9x50 with lesser quality lenses and coatings.

quote:

Originally posted by stubblejumper:
If all lenses and coatings were equal,the calculations would work.However,since lenses and coatings vary so much,a scope that should be brighter according to the calculations,may not actually be as bright.For example 3x9x40 with great lenses and coatings may be as bright or even brighter brighter than a 3x9x50 with lesser quality lenses and coatings.

Amen, brother! And I’ve tested this, the same scope can appear totally different to two different people, or even the same person if he uses his other eye to look through the scope. My left eye gives me the appearance of a slightly brighter image than does my right eye when viewing through the same scope. Not allot, but certainly noticeable.

Thanks Rick 0311

I want to compare scopes, not eyes. We can calculate that a 30-06 kicks less than a 375 H&H. Different shoulders will perceive it differently, but all will say the 375 is more. I want to be able to do the same for scopes. I hear your point that some kid could easily make out stuff that I will miss. However, I assume a “brighter†scope will allow both him and I to see with less light than a “dim†one, even though he may be able to see in less light with the dim one than I could with the bright. I know what I can see with the scopes I have and I would like to equate that with others I’m shopping for. Looking through all of them at different light conditions is not possible usually as they won’t let you take them out of the store. Over the net you can’t even see the thing before buying it.

Would multiplying the theoretical “Relative Brightness†by the “% total light transmission†take into account the problems with coatings?

Is there anyway, prior to buying both and taking them into the woods, of telling if a 3x9x50 VX1 would perform better than 3x9x40 Fullfield-2? Or telling if they would be better or worse than my VX2 2x7x33 which I have experience with?

makeminestainless,

Sorry, I thought you wanted a practical answer and not a theoretical one.

Yes, in “theory’ you can do the math I listed and it will give you a “theoretical†difference in the scopes “relative brightness.â€

In general terms, all other things being equal, a larger objective lens will give you a slight advantage in dim light conditions at any given magnification. How much advantage?...I can’t say, and I do not know of any easy way to tell other than looking through the scope and comparing it to another one.

I’m sorry to keep bringing up things that you obviously don’t want to consider, but % of light transmission is not always figured the same by each of the manufacturers. Some state a figure, but don’t bother to tell you that it is for each lense/air space in the scope. Then it will be up to you to figure out how many lenses are in the scope and again do some math to figure out what’s actually coming out the ocular lens to your eye.

What you might consider is asking the company you deal with what their return policy is if the scope has been taken out of the box but not mounted. Then you can check it against the scope you have and return it if it doesn’t meet your expectations or requirements.

Beyond this I really don’t know how to answer your question any other way.

Reality is the ultimate judge over theory.

Rick is our resident expert here, but I tend to look at 3 things

1. Manufacturer. Don't kid yourself, you get what you pay for and names like Zeiss, Swarovski and Kahles do mean a lot.
2. Twilight Facgtor. The square root of power times objective diameter. This take into account the fact that you can distinguish objects in low light better at 12 power than 9 power, all other factors being equal.
3. Field of view. I like the widest field of view possible at the lower power of a variable scope. It helps you find the game quickly and hit running shots if necessary. Scopes with a wide field of view are generally the scopes that give you an instant picture when you throw your rifle up, you don't have to move your head around in order to find a clear picture in the eye box.

JMHO

woods,

About the only than I am an expert on is messing things up most of the time, but I’ve pretty much got that down pat!

I have played around with and tested/compared lots of optical stuff over the years and if I have learned one thing it is that the biggest variable is not in the scope...it’s about 3 inches behind it!

I’ve also learned to take the advertising terms and claims of manufacturers with a very large grain of salt.

Did you notice that when the theory and calculations are discussed, the term "all other things being equal" is always mentioned.The truth is that where lenses and coatings are concerned "all things are not equal".There is no method to "accurately" calculate the brightness of a scope,no matter how much you wish that there was.

quote:

Originally posted by stubblejumper:
Did you notice that when the theory and calculations are discussed, the term "all other things being equal" is always mentioned.The truth is that where lenses and coatings are concerned "all things are not equal".There is no method to "accurately" calculate the brightness of a scope,no matter how much you wish that there was.

I agree, that phrase is used as a qualifier to discuss things in “general†terms, not technical terms. I had already gotten the distinct impression that the gentleman wasn’t real interested in “technicalities†so that’s why I used it.

quote:

I had already gotten the distinct impression that the gentleman wasn’t real interested in “technicalities†so that’s why I used it.

I also get the distinct impession that he does not want to accept the fact that there is no accurate way to calculate the brightness of a scope.

quote:

Originally posted by stubblejumper:

quote:

I had already gotten the distinct impression that the gentleman wasn’t real interested in “technicalities†so that’s why I used it.

I also get the distinct impession that he does not want to accept the fact that there is no accurate way to calculate the brightness of a scope.

Does sort of sound that way doesn’t it?

quote:

Originally posted by Rick 0311:

quote:

Originally posted by stubblejumper:

quote:

I had already gotten the distinct impression that the gentleman wasn’t real interested in “technicalities†so that’s why I used it.

I also get the distinct impession that he does not want to accept the fact that there is no accurate way to calculate the brightness of a scope.

Does sort of sound that way doesn’t it?

Actually I am interested in “technicalitiesâ€, but you're correct that I think there should be some way of getting a rough sort on these prior to purchase.

OK then... Any good sources that rate scopes? Or is it so subjective that all of us have to do our own?

Thanks guys.

makeminestainless,

He's probably going to hate me for suggesting this, but if it were me I would contact Jon at The Optic Zone.

Jon is as honest as the day is long and he is not going to try and sell you something you don't want or need.

Unlike allot of dealers Jon seems to actually handle and look through the products he sells and I believe he would give you as honest an appraisal on the different scopes as just about anyone out there.

Be a classy guy though if he helps you give him your business.

quote:

Exit pupil diameter= Objective lens diameter (in mm’s) divided by the magnification of the scope.

What difference does the tube sise make in this then? I have a straiht Tube 30mm 1.5X4.25 that seems to pick more light than my 6x16 1 in tube 40mm?

Lets confuse it even more.

quote:

What difference does the tube sise make in this then?

Really,none.in fact some companies like leupold use 1" internals in their 30mm scopes.The larger diameter tube provides more adjustment and is stronger.

quote:

Originally posted by invader66:

quote:

Exit pupil diameter= Objective lens diameter (in mm’s) divided by the magnification of the scope.

What difference does the tube sise make in this then? I have a straiht Tube 30mm 1.5X4.25 that seems to pick more light than my 6x16 1 in tube 40mm?

Lets confuse it even more.

Easy to answer. Tube diameter has no impact on optical performance. Larger tube diameter only aids in additional adjustments.

quote:

OK then... Any good sources that rate scopes? Or is it so subjective that all of us have to do our own?

Well if you do folow these and other forums you will see trends.One of them is that in low priced scopes, most posters state that the bushnell elite series are quite bright.As the price increases many people feel that the ziess conquest is very bright for the money.At the top end,most people favour ziess,swarovski and schmidt&bender.Not scientific by any means,just the general concensus of the posters.

quote:

Originally posted by invader66:

quote:

Exit pupil diameter= Objective lens diameter (in mm’s) divided by the magnification of the scope.

What difference does the tube sise make in this then? I have a straiht Tube 30mm 1.5X4.25 that seems to pick more light than my 6x16 1 in tube 40mm?

Lets confuse it even more.

Gene,

There are other factors (like the huge difference in magnification between those two scopes) at work because the tube size has no measurable effect on light waves passing through the scope.

The 30mm tubes allow for a bit more erector tube movement so they might give more adjustment range, but as far as light transmission goes there is no difference.

I'm not going to be any help, but that's normal.

The cheapest scope i'v ever bought seems to be the clearest/brightest to me.

Practicly, we get a scope to put on a rifle and shoot. The difference in clarity may matter for a few minutes a day.
What I want is accuratly shifting adjustments, water/fog proof, general toughness, and no variation of POI if changing power.
To me, light gathering is sales speal, and every manufacturer seems to have the "Clearest".

Cripes,if you got the dearest one you want or can afford you'd be right to go.

Awhile back I had a conversation with the owner of US Optics about this very subject. He said that everyone can get great glass today,the difference is in the way the lenes are handled and installed and that is what makes the difference also he said that Us Optics used larger internal lenes than S&B and this also aids in optic quality.He also said that tube diamiter only aided in allowing more internal adjustments not in brightness or resilution

quote:

The difference in clarity may matter for a few minutes a day.

And those minutes are the first minutes in the morning and the last minutes in the evening during which time I kill the majority of my elk and deer.I have passed up animals during legal time because my scope was not bright enough to allow me to place the crosshairs properly.A small difference in brightness can make a huge difference in a hunters success.

quote:

Originally posted by stubblejumper:

quote:

The difference in clarity may matter for a few minutes a day.

And those minutes are the first minutes in the morning and the last minutes in the evening during which time I kill the majority of my elk and deer.I have passed up animals during legal time because my scope was not bright enough to allow me to place the crosshairs properly.A small difference in brightness can make a huge difference in a hunters success.

You are spot on

quote:

Originally posted by stubblejumper:

quote:

The difference in clarity may matter for a few minutes a day.

And those minutes are the first minutes in the morning and the last minutes in the evening during which time I kill the majority of my elk and deer.I have passed up animals during legal time because my scope was not bright enough to allow me to place the crosshairs properly.A small difference in brightness can make a huge difference in a hunters success.

Thank you. Doesn’t anyone hunt in the woods or on overcast days? I don't think this subject is trivial.

I also don't believe that more expensive is necessarily better, particularly on the lower and middle price range. I think the new Leopold’s are better, but I know when I first got a cheapo 3x9x40mm Bushnell Banner “Dust to Dawn†to put on a cheap gun, I was amazed how much later I could see than with same dimension Vari-X-2. Granted the durability was not there, but for a light kicker I think it would actually be a superior scope, for not even 40% the price. Makes we wonder what kind of a bargain the Legends are.

I don’t recall anyone claiming that the most expensive scopes were always the brightest, or that brightness didn’t make any difference.

What several of of have tried to do is to correctly answer your original question as to whether or not there was a quick math formula that you could use to determine which scope was going to be brighter (to your eyes).

I gave you the formula for exit pupil size and relative brightness but felt it would be helpful that you know up front that the formula does not (and cannot) include many of the variables that will determine the actual brightness that your individual eye will perceive.

quote:

Originally posted by jwp475:

quote:

Originally posted by Rick 0311:
I don’t recall anyone claiming that the most expensive scopes were always the brightest, or that brightness didn’t make any difference.

What several of of have tried to do is to correctly answer your original question as to whether or not there was a quick math formula that you could use to determine which scope was going to be brighter (to your eyes).

You are spot on US Optics claims as well as those that use them that a 44mm objective from US Optics will equall or surpass a Nightforce or S&B with a 56mm objective and if true that alone would shoot down the math aspect of figureing light gathering ability

I gave you the formula for exit pupil size and relative brightness but felt it would be helpful that you know up front that the formula does not (and cannot) include many of the variables that will determine the actual brightness that your individual eye will perceive.

spot on

I’ve got some very sensitive photographic light meters with spot metering capabilities that can detect changes in light so small that the human eye could never notice them.

Many times optical manufacturers use figures obtained by optical measuring devices that would make my light meters look like horse a buggy stuff by comparison, and while impressive for sales literature can’t really be realized by us mortal humans.

I don't want to hijack the thread ... but a point has been brought up that I remain very curious about ... and that is, the 30mm tube vs. the 1" tube. I completely understand that in MOST cases, the same size and quality erector set and internals are used between the two, thus granting the 30mm tube more room for adjustments. I also understand that the larger diameter tube is more rugged structurally. Now, before I get to my question, please note that I've already admitted to knowing that the same erector/internals are used between the 30mm and 1" tubes ... but sometimes, the 30mm tubes DO have larger lenses ... Having said that, I want to ask my question ...

How much larger would the maintube (and erector/internals) have to be (over a 1" or 30mm) to make a noticable difference in "brightness" or "light gathering"?

I'm assuming that the reason there's no difference in brightness between the 30mm and 1" tubes because of A) most of the time it's the same erector/internals, and B) because the actual size difference between the two is not that great. However, I would have to think, logically, that at some point along the scale, an increase/decrease in maintube diameter (thus increase/decrease in the size of the erector/internals) would come into play... Does anyone know if this is the case, and if so, how much larger/smaller would the maintube diameter have to be before the difference became aware to the human eye?

A 56mm diameter straight tubed scope will produce the same sized exit pupil as a one inch tubed scope (or any other size tube) with a 56mm objective, and having the the same magnification.

A few observations that may or may not be to the original point.

IMO the best way to determine how usable a scope is in twilight is determined by 2 things, 1 exit pupil - divide the objective by the magnification. Young eyes can use up to a 7 fully anything under 4-5 starts getting dark early. Quality of the scope, you can see better in the dark with a 3-10x40 of top manufacture than you can with a 3-10x50 of a lesser end manufacture.
The places I've hunted worst light is best time for deer.
30mm tubes may not theoretically have some advantages but for whatever reason (better glass, higher resolution etc.) the seem to be better optically. Maybe they just better glass in the highest end scopes.
You are better off hunting with an inexpensive rifle and a high end scope than with a high end rifle with an inexpensive scope. An inexpensive Savage or Tikka might shoot just as well has a Dakota or Sauer but Simmons Scopes aren't Swarovski's and Busnell's aren't Schmidt und Benders.......................DJ

quote:

Originally posted by djpaintles:
A few observations that may or may not be to the original point.

IMO the best way to determine how usable a scope is in twilight is determined by 2 things, 1 exit pupil - divide the objective by the magnification. Young eyes can use up to a 7 fully anything under 4-5 starts getting dark early. Quality of the scope, you can see better in the dark with a 3-10x40 of top manufacture than you can with a 3-10x50 of a lesser end manufacture.
The places I've hunted worst light is best time for deer.
30mm tubes may not theoretically have some advantages but for whatever reason (better glass, higher resolution etc.) the seem to be better optically. Maybe they just better glass in the highest end scopes.
You are better off hunting with an inexpensive rifle and a high end scope than with a high end rifle with an inexpensive scope. An inexpensive Savage or Tikka might shoot just as well has a Dakota or Sauer but Simmons Scopes aren't Swarovski's and Busnell's aren't Schmidt und Benders.......................DJ

Exactly

quote:

Originally posted by djpaintles:
A few observations that may or may not be to the original point.

IMO the best way to determine how usable a scope is in twilight is determined by 2 things, 1 exit pupil - divide the objective by the magnification. Young eyes can use up to a 7 fully anything under 4-5 starts getting dark early. Quality of the scope, you can see better in the dark with a 3-10x40 of top manufacture than you can with a 3-10x50 of a lesser end manufacture.
The places I've hunted worst light is best time for deer.
30mm tubes may not theoretically have some advantages but for whatever reason (better glass, higher resolution etc.) the seem to be better optically. Maybe they just better glass in the highest end scopes.
You are better off hunting with an inexpensive rifle and a high end scope than with a high end rifle with an inexpensive scope. An inexpensive Savage or Tikka might shoot just as well has a Dakota or Sauer but Simmons Scopes aren't Swarovski's and Busnell's aren't Schmidt und Benders.......................DJ

I couldn’t agree more. Optics are not the place to try and save your money.

However, on the topic of tube size, I have some Unertl’s with one inch tubes and the optical quality and brightness is about as good as it gets. I have compared them side by side with similar magnification and objective lens sized scopes with 30 mm tubes and don’t see a bit of difference.

quote:

Originally posted by Rick 0311:

However, on the topic of tube size, I have some Unertl’s with one inch tubes and the optical quality and brightness is about as good as it gets. I have compared them side by side with similar magnification and objective lens sized scopes with 30 mm tubes and don’t see a bit of difference.

Unertl's are probably the exception that proves the rule................DJ

quote:

Originally posted by djpaintles:

quote:

Originally posted by Rick 0311:

However, on the topic of tube size, I have some Unertl’s with one inch tubes and the optical quality and brightness is about as good as it gets. I have compared them side by side with similar magnification and objective lens sized scopes with 30 mm tubes and don’t see a bit of difference.

Unertl's are probably the exception that proves the rule................DJ

In fact, some of my brightest Unertl’s have 0.750 inch tubes. Some of them babies are so bright I have to wear sunglasses so I don’t blind myself!!!

Rick

I realize that regardless of the maintube diameter with respect to the objective/occular diameter, that the "exit pupil" size will not change ... However, wouldn't it stand to reason that if you had (for example) a 34 or 35mm maintube, with larger erector lenses, that the clarity and resolution could be dramatically increased because of the size of the lenses? I mean, I've heard a LOT that one of the main problems with lenses (regardless of size) is that they are ground down on the edges to make the perfectly circular, and the right diameter ... and further, this process of making and "honing" the lenses is what can cause the "edge to edge" clarity degrade ... So if that's true, wouldn't the larger lenses in the erector of a larger maintube be capapble (all other things being equal ... LOL) of producing a better image in the end?

I think all of us that have looked thru more than a few scopes have found that most are pretty clear in the center of the field of view ... but not that many are truly clear from edge to edge, at all magnifications ...

WGM,

Since all we are really dealing with and discussing is “theory’ then Yes...â€theoretically†what you said is true.

We are all talking about Light and what happens to it when it passes through a rifle scope... so perhaps it would be helpful to discuss exactly what this light thing actually is.

If you have ever played with an optical prism you will know that when a beam of white light is projected through an optical prism a rainbow of colors comes out the other side. Each of the colors has a different wave length...Blue has the shortest and Red has the longest.

Each of these wave lengths will be bent differently when they strike and pass through a lens. The shorter being bent more severely than the longer. In addition, light rays entering the furthest from the optical axis (the center of the lens) will also be bent more severely than those striking the lens closer to the center. In other words, a ray of any color of light entering the lens at the edge will be bent more than a ray of the same color light entering closer to the center of the lens.

To get all these errant light rays that are being scattered all over the damned place inside the scope to converge at a common point ain’t easy. Scope manufacturers use combinations and groups of different types of glass, different shapes (flat, convex, concave) and different coatings on the glass to compensate for all this unequal bending and to wrangle all these scattered light rays back to where they all come together at two common points in the scope...the first focal plane and the second focal plane. Actually, there is sort of a third spot but its not inside the scope it is behind the ocular lens where the exit pupil is focused and where we place our eye to see the image.

The quality of the materials used (glass and coatings) and the accuracy of the placement and matching of the lenses is what gives a scope clarity (resolution), edge to edge sharpness, and brightness. Size of the lenses inside the scope alone cannot provide a better or brighter image.

My Unertl scopes with 0.750 inch tubes and 41mm objectives will rival the edge to edge sharpness and the resolving power of allot of scopes I have seen that have gigantic 56mm and 58mm objective lenses and 35mm tubes. And if the magnification is the same the brightness ain’t all that different either.

Some makers of cheaper scopes though have followed your logic and they sometimes place what amounts to a big washer behind the objective lens that only allows light rays to enter close to the optical axis (the center) of the lens, because the edges of their lenses are crap and they know it.

quote:

Originally posted by stubblejumper:

quote:

The difference in clarity may matter for a few minutes a day.

And those minutes are the first minutes in the morning and the last minutes in the evening during which time I kill the majority of my elk and deer..

Sure, but to get away from all the techno stuff,
your sure stretching my imagination.

IE So you stumble over your stubble in pitch black to get into Elk home ground by first light and wow there he is. Usually in the first few minutes of half light. I'm wondering where he was that you find him just nearly always in half light??
Anyway it saves having to hunt all flamen day.

Now this elcheapo no mame scope I had I could see a dingo in moonlight. Couldn't see the fine crosshairs, but it seemed the course ones just pointed at the centre.

And funny, the deer here seem to be in the forest all bloody day wandering around all over the place. Cripes ya can shoot the damn things with an old mil. clunker with iron sights.

Still, if you have to have the best, Swarovski,Zeiss,Kahles etc. will be glad to take your money off ya.
Then all you have to worry about is finding the deer and hitting 'em. A minor problem, compared to a less than perfect lense edge.
Gimmy a break fellers.

quote:

IE So you stumble over your stubble in pitch black to get into Elk home ground by first light and wow there he is. Usually in the first few minutes of half light. I'm wondering where he was that you find him just nearly always in half light??

It's called spotting your game beforehand so that you know where they usually are at first light.