Parallax

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Bucksnort1

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Will someone please explain what parallax is relative to rifle scopes? I've read several "on-line" articles about this but I still don't know exactly how it works. I do know it can change the strike of a bullet on a target from one round to the next.

In Denver, on Sunday mornings, there is a talk show called, "Stump the Professor". He takes questions on all sorts of science topics. The problem for me is, when he explains most things, he isn't talking to me, he is talking to Albert Einstein. Some people have called me Einstein but I don't think it is the way I want. I think you get the point. When you explain this, do it the Army way and use the KISS principle - Keep It Simple Stupid. I'm not saying any of you are stupid. I think you get the point. Here are a couple of questions.

Is parallax only a problem with scopes greater than 9X and is this the reason most of the scopes hunters and others buy, are not greater than 9X?

Can a variable 9X scope be reduced in power and eliminate parallax?

I'm sure the price and quality of the scope has an effect on this.
 
Quote from a Leupold owners manual, pages 27 and 28.

http://www.leupold.com/wp-content/uploads/2012/07/Tactical_Scope_Manual.pdf?c9f52e

UNDERSTANDING PARALLAX
Parallax is the apparent movement of the target relative to the
reticle when you move your eye away from the center point of the
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eyepiece. It occurs when the image of the target does not fall on
the same optical plane as the reticle. This can cause a small shift
in the point of aim. Maximum parallax occurs when your eye is
at the very edge of the exit pupil (Even in this unlikely event, our
4x hunting scope focused for 150 yards has a maximum error of
only 8/10ths of an inch at 500 yards). At short distances, effects
of parallax do not affect accuracy (using the same 4x scope at 100
yards, the maximum error is less than 2/10ths of an inch ). It is
also good to remember that, as long as you are sighting straight
through the middle of the scope, or close to it, parallax will have
very little effect on accuracy.
INSTALLING
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In a nutshell unless you are trying to shoot tiny targets with poor form it will never be an issue.
 
If you go outside and look at a rock that is 50 yards away, and have a tree which is 150 yards away behind that rock. You will notice that you are only able to focus your eyes on one of these objects. You will be able to see the other, but not as sharply. This is because they are not in the same viewing plane.

When you look through a rifle scope it's sorta the same. The scope is set to have the cross hairs parallax free at a set range (say 100 yards), at this range the optics have given the illusion the crosshairs are actually on the target at this range, they are both in the same plane, but anything outside of this range the cross hairs will appear to float and will not sit perfectly on the target.
So if you are looking at a target that is 300 Yards away and your scope is set to be parallax free at 100 Yards, you have the situation like the tree and the rock.

This will happen with any scope, but it isn't as noticeable with a lower magnification, so they don't bother making it adjustable. Sometimes with a 9x scope you will notice parallax, but generally you aren't busting crows at 400 yards with one, so it isn't usually a problem.

The error that is induced by the cross hairs and the target being not in the same plane can be more or less nullified, but having a proper check weld and having your head in the exact same spot for every shot.

Parallax error is pretty obvious when you re in a situation where it is wrong. So I'd say don't worry about it, if it's never effected you before then it probably doesn't matter. But if you have noticed it being a problem, then you will need to buy a scope that adjusts for it.
 
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The parallax condition exists when, with the rifle in a solid rest and the shooter aiming at a certain point, the target seems to move sideways if/when the shooter's eye (head) is moved sideways, towards one side or the other.


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jmr40. Your first sentence is the explanation I have been seeking. This is what I thought it was and I believe, at sometime in the past, I conducted an experiment on a scope and noticed the effect.

A number of years ago, a friend and I were attempting zero his Remington -06. Bullet strikes were all over the target. I convinced him to buy a better scope (Leupold), which solved the problem. I don't know if his problem was related to the cheap scope that came with the rifle. I don't recall scope manufacturer. I'm having a similar problem with a single shot .243 but I have a feeling it was the brisk wind during a recent zero session.
 
In a nutshell unless you are trying to shoot tiny targets with poor form it will never be an issue.
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I would have to disagree with that - I think parallax error accounts for huge misses at shorter ranges (under 75 yards) for a lot of people (who end up thinking it's the rifle, or the ammo, or a bad hold).... It's a very important thing. Sure, perfect form eliminates it, but perfect form is hard to get.
 
How much parallax error is there at 50 yards for a 16X scope with a 50 mm objective lens focused at infinity?
 
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I would have to second Unlicensed's comment. Awhile back I placed the parallax equation on an Excel workbook and charted bullet placement for a given "bad form". I was surprised at how little off center the eye had to be in order to throw the bullet off the intended POI.

I have the workbook posted on my personal web site if anyone wants to look. It's a WIP that I just never got back to. It ain't pretty, but it works. http://www.fshrmen.net/tag/parallax/
 
Bart B. said:
How much parallax error is there at 50 yards for a 16X scope with a 50 mm objective lens focused at infinity?
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16 mm / .63" with an eye offset of just 1mm. That would be a total parallax error of 1.26", left to right or high to low.

If you really had your eye way offset to the maximum for that objective and magnification (where you could just barely see the intended POI) then the total would at most be 1.97".

Of course these are optical values and don't factor in the person, the rifle, the bullet, the wind, etc..
 
With that scope I referenced focused at 200 yards, the error will much less at 50 yards. So I don't think parallax is a big issue. Most folks have their aiming eye centered in the middle half of the exit pupil anyway.
 
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Bart B. said:
With that scope I referenced focused at 200 yards, the error will much less at 50 yards. So I don't think parallax is a big issue. Most folks have their aiming eye centered in the middle half of the exit pupil anyway.
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My understanding is that if the eye is properly centered then parallax is a non-issue. But with a parallax setting of 200 yards, the target at 50 yards, and the offset just 0.5 mm from the optical axis then the shot will be off 1/4". Of course it will be less if the scope has a fixed parallax of 150 or 100 yards as do many centerfire scopes, and near zero for rimfire scopes that normally have a parallax setting of 60 yards.
 
As there is no parallax when the aiming eye is in the optical axis and there is when it's not, parallax is only "adjusted" by moving the eye at right angles to the line of sight. Regardless of what's spoke or in print, no scope is adjusted for parallax because their lenses move in the line of sight axis and that focuses the target image on the reticule for different ranges. Exactly like camera lenses focusing images on film or sensors.

Objects closer than those at the range the scope's focused at are in focus behind the reticule. To make them focused on the reticule, the scopes front objective lens group had to move forward closer to the target to move its focus forward onto the reticule. Objects further than the range the scope's focused at are in focus in front of the reticule. The objective lens group has to move back to focus them on the reticule.

This is why objects closer than focused range appear to move to the left of the reticule as the eye is moved to the right. And why objects further than focused range appear to move to the right of the reticule when the eye is moved to the right.

It's my opinion that all the talk and print about setting and adjusting parallax has caused more confusion, misunderstanding and contradictions of optical physics. And scope makers compounded the confusion when incorrectly stating their scopes adjust parallax and others correctly say their scopes focus for target range.
 
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Lets clear up one huge misconception.
"There is no Parallax when having the eye on the optical axis".

Rubbish!

Parallax is the 2 planes of focus being out of position LENGTHWISE It has absolutely nothing at all to do with any kind of horizontal movement in any way.

You won't see the offset, but it is absolutely 100% guaranteed to be there. It only becomes noticeable when you have the eye off center though.
 
wogpotter, wanna bet ten million on that?

I think you're thinking 90 degrees out of phase.

Targets 3 different ranges away but in line with each other will have their images focused 3 different distances about the reticule. If the middle target is where the scope's focus is at, it'll be focused on the reticule at its center on the optical axis, the furthest target will be focused on the optical axis in front of the reticule further from the aiming eye and the closest target will be focused on the optical axis behind the reticule closer to the aiming eye. They're all in a straight line on the optical axis. With the aiming eye on that same axis, they'll align one atop the other. When the aiming eye's off to the right, the furthest target image will appear to the right of the reticule and the closest target to the left of the reticule.
 
I can't speak to the physics of the matter. Conceptually I can see that parallax exists when there is no eye offset from the optical axis. But from what I can tell using the parallax formula I referenced, there doesn't seem to be any measurable change to the POI when there is no eye offset. (I'd love to know if this understanding is incorrect.) Changes in the POI is what I will be interested in understanding.

I went ahead and graphed my understanding. I chose a common centerfire scope parallax setting of 100 yards and a common objective size of 44 mm. I assumed an eye offset of 1 mm. Having grown up with inches and feet, it's easier for me to visualize fractions of an inch, so let's call that 1 mm equal to 1/24". In the chart, I rounded all values to the nearest 1/16". I displayed the values for the scope set at 5x and at 20x. The values shown are just for one direction of offset. If one considers total offset from left to right (or up and down) then double the values shown on the chart.

In a hunting scenario, I can see it being quite realistic for the eye to be 1/24" off from the center of the objective. That said, with the scope described above I can see me missing a prairie dog at 200 yards when parallax deviation is added to other common factors.

 
SerenityNetworks, I think you'll grasp this parallax thing a lot easier if you don't think about adjusting parallax.

What's done is, the scope is focused at some downrange point. 100 yards, per your example. The target image at that range will be focused some distance behind the objective lens. And when focused at 100 yards, the target image will be focused on the reticule.

If the scope's pointed at a target 50 yards down range, its image will be focused closer to the aiming eye (further from the objective lens) and a ways further back from the reticule. The opposite happens if the scope's pointed at a target 200 yards down range; that target's image will be focused closer to the scope's objective lens and on the other side of the reticule.

The following is based on a rifle scope’s eyepiece focal length to be 2 inches; typical for most scopes. And the objective lens is moved back and forth to get focus on the target. The objective lens system is a telescopic one wherein the physical length is shorter than the optical length. Just like a 200mm (8 inch) camera telephono lens being only 100mm (4 inches) long phycally. The lens groups inside focus images and size them different ways in telephoto lenses compared to long lenses. A 200mm long lens will be physically 200mm (8 inches) long. And a scope's magnification is calculated by dividing the objective lens group focal length by the eye piece lens focal length.

A 5X scope will have target images at different ranges focused this far behind the objective lens group:

Infinity, 10.000 inches
1000 yards, 10.003 inches
500 yards, 10.006 inches
300 yards, 10.009 inches
200 yards, 10.014 inches
100 yards, 10.028 inches
50 yards, 10.037 inches
25 yards, 10.056 inches

A 10X scope will have target images at different ranges focused this far behind the objective lens group:

Infinity, 20.000 inches
1000 yards, 20.011 inches
500 yards, 20.022 inches
300 yards, 20.037 inches
200 yards, 20.056 inches
100 yards, 20.112 inches
50 yards, 20.149 inches
25 yards, 20.225 inches

A 20X scope will have target images at different ranges focused this far behind the objective lens group:

Infinity, 20.000 inches
1000 yards, 40.045 inches
500 yards, 40.089 inches
300 yards, 40.149 inches
200 yards, 40.224 inches
100 yards, 40.450 inches
50 yards, 40.602 inches
25 yards, 40.909 inches

For example, a 10X scope focused on a target 200 yards away, its image will be focused on the reticule when its objective lens is moved .056" forward from its infinity setting. With the aiming eye at any place in the exit pupil’s field of view off the optical axis, the target will not move relative to the reticule.

Move the target back to 300 yards and its image is now focused in front of the reticule 20.037" behind the objective lens. That’s .019" forward of where the 200 yard target image was focused; it’s in front of the reticule that far. With the aiming eye on the optical axis centered in the exit pupil’s field of view, it will still be aligned with the reticule. Move the aiming eye to the edge of the field of view and that target image will appear to move to the right of the reticule.

Move the target closer up to 100 yards away, its image will be focused behind the reticule, closer to the aiming eye, 20.112" behind the objective lens. That’s .056" closer to the aiming eye in front of the reticule but it’s still on the optical axis. It will appear to move to the left when the aiming eye’s off to the right at the edge of the exit pupil’s field of view.

Note that for side focus scopes, the focal length of the objective lens system is changed to get the same effective shift in target focus on the reticule. Same thing happens with both system types as far as images for different target ranges focussing about the reticule.
 
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wanna bet ten million on that?
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Not just "YES" but Oh hell yes! Show me the stakes first though.:D

My contention exactly rephrased so there's no "misspeak" claim when it comes time to pony up:

"Parallax is hidden by exact on axis viewing but not deleted. It's still there you just can't see it."
 
Let me give you an easy demonstration of parallax, how it works & when it doesn't.

Put an object on a fixed wall, a sticky dot or something.

Back away from the wall about 10~20 feet.

Take your right arm & point it at the "target" keeping the elbow unbent so the "sight" pencil is a far away as possible.
Hold something obvious (like a pencil) pointing vertically up in the hand.

Take your left arm & do the same thing, but bend the arm at the elbow so the second pencil (or whatever) is closer to your eye than the right hand one.

Close or cover your left (or right) whichever is non dominant eye.

Focus on the "target on the wall" & sway just your head from side to side. Note how the "target", right hand pencil & left hand pencil seem to slide sideways in relation to each other.

Now focus on the far pencil & repeat, note how the movement is different in relation to the first "test".

Repeat a third time focusing on the near pencil.

The relative sideways motion & changing positions of the 3 "planes of focus" (target left & right pencil) is parallax.
 
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