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Dumb Question of the Day-FOV calculation

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Topic: Dumb Question of the Day-FOV calculation
Posted By: Trailblazer
Subject: Dumb Question of the Day-FOV calculation
Date Posted: December/08/2014 at 21:54
Tried to research this a bit but came up empty handed.  May sound like a dumb question, but I'm not sure of the answer.

Scopes advertise a specific FOV at 100 yards on a given power, usually highest and lowest.  If I want to know the FOV at 200 and 300 yards, is it as simple as multiplying the 100 yard figure by 2 or 3?

Or is it not a linear ratio like that?  Seems like the FOV would grow by more than double or triple, but maybe not??



Replies:
Posted By: koshkin
Date Posted: December/09/2014 at 05:11

It is a simple linear ratio.

ILya



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Posted By: Trailblazer
Date Posted: December/09/2014 at 07:22
Thanks!


Posted By: Trailblazer
Date Posted: December/09/2014 at 15:55
...on second thought, are you sure it's linear???  Not challenging your knowledge, but.....well.....I guess maybe I am! Big Smile  But not in an argumentative way.


Let's use the example of a Zeiss 5-25x Conquest HD.  Stats show FOV at 100 yards on 25x to be 4.2'.  So if it's linear, then that means FOV at 200 yards = 8.4', and 300 yards = 12.6'.

This seems reasonable until you start thinking that the difference between each 100 yard increment is only 4.2', whether it's between 100 and 200 yards, or between 900-1000 yards.  Hard for me to believe that the FOV increase from 900 yards to 1000 yards would only be another 4.2'.

Maybe I'm wrong...but that just doesn't seem right???


The entire reason I'm asking this question is because I'm considering buying that scope with the RZ-1000 reticle.  Without getting into a debate about SFP ballistic reticles, my concern with this scope is that my particular load comes in at about 24x (nearly full power) for the reticle to be "calibrated" (according to the Zeiss calculator).  It seems to me that's a whole lot of power for the closer ranges, and target acquisition would be tough without constant power changes.  I realize I would still have to make power adjustments even with a FFP reticle, but at least with that setup I wouldn't have to make sure I was on a specific power in order to be accurate.  And then of course there is the whole debate about how accurate the ballistic reticle will be in the real world.

Maybe I'm just trying to talk myself out of it that scope...but I love Zeiss glass.  I have a Vortex Viper PST on order.  It's already been 5 months, and they're saying another 1-3 months.  My biggest concern with the Vortex is that the one I looked through got pretty hazy at the higher powers.  The Zeiss is nice and crisp, but I just don't know about the SFP ballistic reticle.  I would love to try it, but once I mount it, it's mine.  Can't return it.


Posted By: koshkin
Date Posted: December/09/2014 at 16:22
Originally posted by Trailblazer Trailblazer wrote:

...on second thought, are you sure it's linear???  Not challenging your knowledge, but.....well.....I guess maybe I am! Big Smile  But not in an argumentative way.


Let's use the example of a Zeiss 5-25x Conquest HD.  Stats show FOV at 100 yards on 25x to be 4.2'.  So if it's linear, then that means FOV at 200 yards = 8.4', and 300 yards = 12.6'.

This seems reasonable until you start thinking that the difference between each 100 yard increment is only 4.2', whether it's between 100 and 200 yards, or between 900-1000 yards.  Hard for me to believe that the FOV increase from 900 yards to 1000 yards would only be another 4.2'.

Maybe I'm wrong...but that just doesn't seem right???


The entire reason I'm asking this question is because I'm considering buying that scope with the RZ-1000 reticle.  Without getting into a debate about SFP ballistic reticles, my concern with this scope is that my particular load comes in at about 24x (nearly full power) for the reticle to be "calibrated" (according to the Zeiss calculator).  It seems to me that's a whole lot of power for the closer ranges, and target acquisition would be tough without constant power changes.  I realize I would still have to make power adjustments even with a FFP reticle, but at least with that setup I wouldn't have to make sure I was on a specific power in order to be accurate.  And then of course there is the whole debate about how accurate the ballistic reticle will be in the real world.

Maybe I'm just trying to talk myself out of it that scope...but I love Zeiss glass.  I have a Vortex Viper PST on order.  It's already been 5 months, and they're saying another 1-3 months.  My biggest concern with the Vortex is that the one I looked through got pretty hazy at the higher powers.  The Zeiss is nice and crisp, but I just don't know about the SFP ballistic reticle.  I would love to try it, but once I mount it, it's mine.  Can't return it.

The FOV is twice wider for a distance that is twice longer.   That is what linear means.

At 200 yards, it is twice wider than at 100 yards.  At 400 yards, it is twice wider than at 200 yards.

At 300 yards, the distance is 1.5 times longer than at 200 yards, so the FOV is 1.5 times wider than at 200 yards.

This is pretty simple geometry.

ILya


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Posted By: Kickboxer
Date Posted: December/09/2014 at 17:29
You didn't even mention string theory...

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There are some who do not fear death... for they are more afraid of not really living


Posted By: Trailblazer
Date Posted: December/09/2014 at 17:51
Originally posted by koshkin koshkin wrote:


The FOV is twice wider for a distance that is twice longer.   That is what linear means.

At 200 yards, it is twice wider than at 100 yards.  At 400 yards, it is twice wider than at 200 yards.

At 300 yards, the distance is 1.5 times longer than at 200 yards, so the FOV is 1.5 times wider than at 200 yards.

This is pretty simple geometry.

ILya



Yes...that's the same thing I said.  It grows by only 4.2 feet for each 100 yards.  The math works out the same.   The increase between each 100 yard increment is only 4.2 feet, whether between 100 and 200 yards, or between 900 and 1,000 yards.  Still doesn't seem quite right, but perhaps it is.

I understand what "linear" means....that's why I asked if it was linear!  The question wasn't what linear means...the question was IS it's linear.  I'll take your word for it that you're right, but I may have to throw a challenge flag! 

The FOV from the scope to whatever the distance in question is represents an isosceles triangle.  There can be only one isosceles triangle at which the altitude (in this case the distance to target) would equal the width of the base (in the case the FOV), and that is where the peak of the triangle is at 90 degrees.  So I guess my question is...is the FOV ALWAYS at 90 degrees on every scope, every time?



Posted By: Trailblazer
Date Posted: December/09/2014 at 17:56
...To correct myself, I meant to say is the base is twice that of the altitude, not the same as.


Posted By: Trailblazer
Date Posted: December/09/2014 at 18:24
O.K., I did some more thinking, and I believed I answered my own question.

It is NOT linear.  This can be proven by looking at the stats of different scopes that have the same zoom range and objective lens size.  Again, the only way it could be linear is if the FOV is a right isosceles triangle, and if this was always the case, then every scope with the same objective size would have the same FOV at 100 yards as every other scope if they were on the same power.

I think the way to calculate the FOV at various ranges would be to take each individual scopes FOV stats for the maximum and minimum power, and use that to figure out the angle at the peak of the  triangle.  Given that angle, you could then calculate the base of the triangle (FOV) at each given altitude (range).


....pretty simple geometry, really.  Big Grin


Posted By: Trailblazer
Date Posted: December/09/2014 at 19:22
...but then again...the scope length (distance between the glass) could be the reason for the different specs, but I don't think so.  Still don't think it's linear.


Posted By: SEMO Shooter
Date Posted: December/09/2014 at 20:08
I had a Conquest 4.5-14x50 with the Rapid Z 1000 reticle.  I seldom trade or sell my scopes.  But that was one I traded.  The scope itself was fine, but the Rapid Z reticle did not match my loads very well. The reticle was ok for plinking steel, but not for serious longer range accuracy.


Posted By: Trailblazer
Date Posted: December/09/2014 at 20:10
What did you replace it with?


Posted By: SEMO Shooter
Date Posted: December/09/2014 at 20:29
I ended up trading it and some cash for a Nighforce.  I would have been happy with that Zeiss if it had a  plex reticle.  I did not find the Rapid Z 1000 reticle useful for my type of shooting which is 100 to 700 yard target shooting.  I still have 5 Conquest scopes so I'm not a Zeiss hater.  I have a 3-9, 3.5-10, two 4.5-14, and a 6.5-20.  All have plex reticle except the 3.5-10.  It has a #58 ZRF reticle.


Posted By: Trailblazer
Date Posted: December/09/2014 at 20:38
Did you play with the magnification to try to dial the reticle in?
How far off  would you say the reticle was in the 400+ yard range?  Within 4" or so?  Very curious about this because I wouldn't be using it for precise target shooing.  I would be using it for shooting steel, and possibly medium range hunting. 

The 14x wouldn't be so bad, but the RZ1000 only comes in the 5-25x HD now.  Can't get a lower power range. 


Posted By: SEMO Shooter
Date Posted: December/09/2014 at 21:45
I played with the magnification ring.  It was within 4" at 400 yards with Federal 168 grain match.  It is supposed to be calibrated to work with 168 & 175 grain match ammo.  Who's match ammo, and what velocity does it match?  If you load your own will your loads match the ballistics needed?

Your hunting loads will have quite different ballistics that will not match up as well.  Do you think you would actually take a longer shot than 300 or 400 yards?  The center line of the reticle is for 500 yards with 100-400 all above center.  Lots of lines and a very busy reticle.

Have you considered a Rapid Z 600?  It is much simpler.  I am not saying the Rapid Z 1000 won't do what you want, but it is not a magic answer to making an acceptable hit at longer distances.




Posted By: Trailblazer
Date Posted: December/11/2014 at 07:49
All of the points you make are reasons I'm second guessing it.  The rifle is mainly used for having fun plinking steel at various ranges, all while practicing ranging and trying to get shots off quickly.

For the hunting aspect, I realistically wouldn't shoot past 450 yards, and even that may never happen.  I know my limitations and don't want to wound an animal.  The only reason I would even consider it is because my practice range and the field I would be hunting in are the same field, so I will have practiced at every distance within that area. 

As far as the RZ-600 is concerned, I have a Conquest 3-9 with the RZ 600 on top of my -.06.  That reticle doesn't match any of my .308 loads very well, at least according to the calculator.  The optimum power setting isn't high enough for longer range shots (even on the higher power scopes).  It's exactly the opposite problem as with the RZ-1000.

I think I'm just going to cancel the order and wait for the Vortex to come in.


Posted By: SEMO Shooter
Date Posted: December/11/2014 at 08:01
I think you will be quite happy with he Vortex.  One of my buddies has a Viper PST mounted on his Savage 260 and I like his scope.  He is a good shooter and consistently makes head shots on steel targets at 600 to 800 yards.


Posted By: tucansam
Date Posted: December/12/2014 at 14:10
On a side note, what determines a scope's FOV?  I had my USO SN3 3.2-17x44 at the range today, alongside my friend's Razor HD with a 50mm objective.  He has a 35mm main tube, my USO's is 34mm.

At 20x power, his scope had a wider FOV than my USO at 17x.

What determines that?


Posted By: Trailblazer
Date Posted: December/27/2014 at 11:27
Well, I would say his 50mm objective versus your 44mm would be the biggest reason, but there must be other factors as well.  To a lesser degree, I would have to think that the geometry of the internal components would play a small factor as well.


Posted By: koshkin
Date Posted: December/27/2014 at 13:56
Originally posted by Trailblazer Trailblazer wrote:

Well, I would say his 50mm objective versus your 44mm would be the biggest reason, but there must be other factors as well.  To a lesser degree, I would have to think that the geometry of the internal components would play a small factor as well.

Objective lens diameter has no direct relationship to the field of view.

If anything, it is easier to make a wide field of view scope with a smaller objective lens.

The FOV is determined by the lens presription, i.e. the curvatures of different lenses used, not by their diameter.

Go make a 30mm aperture and put it right up to your 50mm scope objective.  FOV will stay the same.

ILya


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Posted By: Trailblazer
Date Posted: December/27/2014 at 16:40
That makes perfect sense.  But it seems like that blows a hole in your previous statement about the field of view doubling when the distance doubles.  Otherwise, every scope would have to have the same FOV.


Posted By: koshkin
Date Posted: December/27/2014 at 16:45
Originally posted by Trailblazer Trailblazer wrote:

That makes perfect sense.  But it seems like that blows a hole in your previous statement about the field of view doubling when the distance doubles.  Otherwise, every scope would have to have the same FOV.


This makes no sense. Please elaborate.

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Posted By: Trailblazer
Date Posted: December/27/2014 at 17:04
As stated earlier, the FOV on any scope represents a triangle from your scope, to whatever distance we're talking about, be it 100 yards, 200 yards, etc.  There is only one triangle in which base (FOV) doubles when the altitude (distance to target) doubles, and that is  a right isosceles triangle.  Therefore, if that is the ONLY triangle with which the FOV could double as the distance doubles, then every scope would have to have pretty much the same FOV, otherwise, it couldn't be a right isosceles triangle.

Make sense?


Posted By: Trailblazer
Date Posted: December/27/2014 at 17:06
..meaning to fit into your theory of the FOV of any scope doubling when the distance doubles, they would all have to have a FOV that represents a right triangle, which would mean they would all have to be the same.

This is obviously not the case, so therefore I believe your theory is flawed.


Posted By: billyburl2
Date Posted: December/27/2014 at 17:26
Unless of course each scope starts out with a different base FOV, because of the internal prescription of the lenses and how it was put together... Each scope will react to distance exactly the same, it's how the scope is designed and built that sets the initial parameters.

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If it is tourist season, why can't we shoot them?


Posted By: koshkin
Date Posted: December/27/2014 at 17:49
Originally posted by Trailblazer Trailblazer wrote:

As stated earlier, the FOV on any scope represents a triangle from your scope, to whatever distance we're talking about, be it 100 yards, 200 yards, etc.  There is only one triangle in which base (FOV) doubles when the altitude (distance to target) doubles, and that is  a right isosceles triangle.  Therefore, if that is the ONLY triangle with which the FOV could double as the distance doubles, then every scope would have to have pretty much the same FOV, otherwise, it couldn't be a right isosceles triangle.

Make sense?

That is slightly correct and mostly flat out wrong.

The FOV is an angle.  The projection of it onto a plane a particular distance away from the vertex forms a triangle.  That is typically an isosceles triangle (though not necessarily, since I have seen plenty of scopes with asymetric FOV due to manufacturing tolerances).  However, the angle at the vertex, varies considerably from scope to scope and from magnification to the magnification.

The distance to the target plane is the height of the triangle and for ANY triangle, isosclees or otherwise, the length of the opposite side of the triangle (which is the FOV in this cases), doubles if you double the height of the triangle.

That is VERY basic geometry.

I am guessing that you are confusing isosceles triangle with an equilateral triangle.  In an equilateral triangle, the angle at the vertex is always 60 degrees.

Aside from the geometrical considerations, what does any of this have to do with the diameter of the objective lens?

ILya


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Posted By: koshkin
Date Posted: December/27/2014 at 17:52
Originally posted by Trailblazer Trailblazer wrote:

..meaning to fit into your theory of the FOV of any scope doubling when the distance doubles, they would all have to have a FOV that represents a right triangle, which would mean they would all have to be the same.

This is obviously not the case, so therefore I believe your theory is flawed.

Once again, right triangle and equilateral triangle are not the same.

And for the record, this is not my personal theory.  This is how geometrical optics works.  I work withoptical instruments for a living and how FOV works is pretty well established.

ILya 


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Posted By: Trailblazer
Date Posted: December/27/2014 at 19:10
Right...but my point remains the same.   If each scope has a different "base FOV" as you put it, then it's impossible for every scope's FOV to double when the distance doubles as Koshkin suggests.

...or were you referring to something else?


Posted By: Trailblazer
Date Posted: December/27/2014 at 19:13
Originally posted by koshkin koshkin wrote:


Once again, right triangle and equilateral triangle are not the same.

And for the record, this is not my personal theory.  This is how geometrical optics works.  I work withoptical instruments for a living and how FOV works is pretty well established.

ILya 


I never said "right triangle".  Re-read my post.  I said "right isosceles" triangle.  BIG difference.

Let's start from scratch.  Do you disagree that a scope's field of view represents an isosceles triangle?


Posted By: Trailblazer
Date Posted: December/27/2014 at 19:30
Perhaps this will help.  Click on the link below and tell me where I'm wrong.  Perhaps I'm missing something...

Click on the link below (or copy and paste if you can't click on it)

http://www.mathopenref.com/isosceles.html


Point "A" represents the scope, or perhaps your eyeball, or whatever.  (Yes, I realize that the FOV will never come to a sharp point like the tip of the triangle, but I think this still makes my point).  The distance between "B" and "C" in the illustration represents the FOV.  The "altitude" figure on the left would represent the distance to the target.  There is only ONE case in which the base of the triangle would be double the altitude, and that is when the angle at "A" is 90 degrees.  Drag point "A" down so that the altitude is 18 (Half the base which is 36) to see what I mean.  With the angle at "A" set at 90 degrees, the base would double to 72 (double the original 36) if you doubled the altitude to 36, and it would continue to double as the distance doubled.

ANY other angle at "A" would NOT result in the base doubling as the altitude doubles.  Therefore, it doesn't seem as though the FOV on every scope would double as the distance doubles, unless  the peripheral vision while looking through the scope was not a straight line like the sides of a triangle, but rather a curved line similar to a parabola if the angle was greater than 90 degrees, and a line that curves the opposite way if less than 90 degrees. 

http://www.mathopenref.com/isosceles.html



Posted By: Dogger
Date Posted: December/27/2014 at 20:39
I think you had better listen to Ilya on this one otherwise your thread title risks becoming a self fulfilling prophecy.   If you use your triangle calculator you will see how doubling the altitude will double the base as long as you keep the angle at "A" constant.


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God save the Empire!


Posted By: billyburl2
Date Posted: December/27/2014 at 20:48
Originally posted by Dogger Dogger wrote:

I think you had better listen to Ilya on this one otherwise your thread title risks becoming a self fulfilling prophecy.   If you use your triangle calculator you will see how doubling the altitude will double the base as long as you keep the angle at "A" constant.
THIS!
Some scope manufactures even post FOV numbers in degrees. This is the one constant that is fixed by the design of the scope.


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If it is tourist season, why can't we shoot them?


Posted By: Trailblazer
Date Posted: December/27/2014 at 20:51
Originally posted by Dogger Dogger wrote:

I think you had better listen to Ilya on this one otherwise your thread title risks becoming a self fulfilling prophecy.   If you use your triangle calculator you will see how doubling the altitude will double the base as long as you keep the angle at "A" constant.


You are right!  I concede!


Posted By: koshkin
Date Posted: December/27/2014 at 20:52
I am not trying to be mean, but there are a few things you are missing, most notably geometry and optics.

How did you get an idea that the the linear FOV at a particular distance is double the distance to the target? 

There isn't a riflescope in existence for which that is accurate.

Using your terminology, if you double the altitude of the triangle, the distance from B to C, assuming the angles remain the same, will double.

ILya


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Posted By: Urimaginaryfrnd
Date Posted: December/28/2014 at 00:59
So let me get this straight. Point A times point B may or may not equal point C except on alternate Thursdays when a lunar eclipse occurs at which time the point may become pointless or inversely proportional in clarity to M.U.D. (Miscelaneous Undocumented Devices). Therefore in theory: The closer you are to chit, the less chit you can see, and the farther you are from chit the wider range of chit you can see, which means that an optic on an orbiting satelite can see a world of chit.

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"Always do the right thing, just because it is the right thing to do".
Bobby Paul Doherty
Texas Ranger


Posted By: Voodoo6
Date Posted: December/28/2014 at 07:47
I plumb guess I gots ma gizzintus mixed up with ma ciphering.....



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"A prisoner of the white lines on the freeway"


Posted By: Trailblazer
Date Posted: December/28/2014 at 08:45
Originally posted by Voodoo6 Voodoo6 wrote:

I plumb guess I gots ma gizzintus mixed up with ma ciphering.....




That's exactly what happened! Big Grin


Posted By: Rancid Coolaid
Date Posted: December/30/2014 at 10:01
Science is hard.

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Freedom is something you take.
Respect is something you earn.
Equality is something you whine about not being given.


Posted By: RifleDude
Date Posted: December/30/2014 at 11:35


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Ted


Money can't buy happiness... but it's much more comfortable to cry in a Porsche than on a bicycle.


Posted By: Peddler
Date Posted: December/30/2014 at 11:38
Big Grin

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When you are dead, you don't know you are dead.It is difficult only for others.

It is the same when you are stupid.


Posted By: Nixterdemus
Date Posted: October/12/2018 at 10:22
Yes, rise Lazarus rise or was that Vlad the impaler? Perhaps the Mummy would be more PC as I risk peril in awaking the dead thread.

In a variable riflescope specs is ER 3.3-3 imply that at the lowest end of magnification the ER is 3.3mm whilst the highest end ER is 3mm?

Thus in the case of a listed 3.3-3.6 ER the shorter ER would correspond w/the lowest power as the longer ER relates to the highest power?




Posted By: koshkin
Date Posted: October/12/2018 at 12:55
Originally posted by Nixterdemus Nixterdemus wrote:

Yes, rise Lazarus rise or was that Vlad the impaler? Perhaps the Mummy would be more PC as I risk peril in awaking the dead thread.

In a variable riflescope specs is ER 3.3-3 imply that at the lowest end of magnification the ER is 3.3mm whilst the highest end ER is 3mm?

Thus in the case of a listed 3.3-3.6 ER the shorter ER would correspond w/the lowest power as the longer ER relates to the highest power?



Not necessarily.  Typically, eye relief of most scopes is shorter at high power, but there are a few out there with longer eye relief at high power.  Scope manufacturers do not list it in any sort of a consistent manner, so by looking at the specsheet there is not easy way to tell.  Typically, the smaller number is for the highest magnification, but not necessarily.

ILya


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Posted By: Nixterdemus
Date Posted: October/12/2018 at 21:05
Thanks for the reply.  So, my point is moot eh? C'est la vie, mon frere.

Maybe I've distorted yet another personal conclusion as well in which your expertise could be of service. If nothing else freeing me from even more ignorance. No claims to whether or not it'll take.

When looking at specs of variable power riflescopes I multiply each low/high power by its corresponding FOV. I determine bias betwixt the twain by which has the higher value. As a rule the higher power finds favour in a slightly better FOV percentage wise when compared to the lower power/FOV. Or so it seems to me.

I always presumed that was due to the lower magnification having somewhat ample FOV, comparitively speaking, and especially in a SFP a bit extra FOV is handy at maximum power which usually subtends w/reticle at that power.

Any nuggets to be gleaned here or is me wee formula total crappola? I take my results w/a grain of salt. Mainly use it for comparision amongst similar priced optics. 


Posted By: koshkin
Date Posted: October/13/2018 at 18:06
With most scopes, FOV does not scale linearly at low magnifications.  There are some where it does, not with most.  If you start at maximum magnification and measure FOV at intermediary steps as you lower magnification, you will see it change linearly for a while until you get close to the minimum magnification where it starts to deviate from linearity.

That is a form of tunneling where internally, the limiting aperture transitions from one stop to another.  For similar reasons, you will also notice that at low magnification, most scope do not use the entire objective lens.  At high magnifications, the limiting aperture is the objective lens diameter, but at low magnifications, it is some internal aperture that acts as a stop.

Also, many scopes do not have the actual claimed magnification range, so if it is marked 5x to 25x, it is not necessarily a 5x erector ration.  They sometimes round up a little.

ILya




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