I hear the terms Focus and Parallax quite often when talking about rifle scopes. There is often some confusion about they these mean and what they do. Generally there is a mechanism to adjust focus and another mechanism to adjust parallax. To make the confusion worse, adjusting the parallax sometimes has the added confounder of making the object (target) appear to go in and out of focus.
As I understand it:
Focus adjusts the scope to the individual shooter's eye... this is a one time adjustment. (For geezers and wearers of prescription lenses this could be a multiple procedure event if new prescription arrive.) The purpose of this adjustment is to adjust the scope so that the image of the reticle (crosshairs) is properly aligned with the back of the shooters eye.
Parallax adjusts the target to the reticle (crosshair). The target image and the reticle must be on the same focal plane within the scope or there is room for apparent movement of the reticle on the target when the shooter'e eye moves (or is positioned differently at the scope).
Here are a few articles and bits of info on this subject.
From: [email protected] (John Bercovitz)
Subject: scope parallax, was Re: Colt M16A2 vs. Colt AR-15 Delta HBAR
Organization: Lawrence Berkeley Laboratory
There may be a modest amount of confusion out there on the subject of scope parallax. Parallax problems result from the image from the objective not being coincident with the crosshairs. (On high magnifications scopes, the objective is the big end of the scope; vice-versa for low power scopes; in either case it's the guzin end.) If the image is not coplanar with the crosshairs (that is the image is either in front of or behind the crosshairs), then putting your eye at different points behind the ocular causes the crosshairs to appear to be at different points on the target. (The ocular is the guzout end of the scope.) In fact, this is the basis of a test for parallax problems:
Set your scoped rifle on sand bags. Align the scope with the center of the target. Without touching the rifle, move your eye around behind the scope. Do the crosshairs appear to move on the target? If they do, the parallax is not set for the range of the target you are using.
So which way do we move the objective to correct parallax? First hold up the index finger of one hand in front of the palm of the other hand. (You don't have to actually DO it, this a thought experiment.) Let the index finger represent the crosshairs and the palm represent the image plane. If you move your head to the left, the finger moves to the right against the palm. So if your crosshairs move to the right on the target's image when you move your head to the left, the image plane must be further away than the
crosshairs. What's a mother to do? Why pull the image plane in a little by screwing the objective bell in so that the objective moves closer to you, of course. In this set up, the image is essentially tied to the objective so moving the objective 0.1 mm moves the image 0.1 mm. And no, the ocular
doesn't change this scenario any more than putting a weak loupe to your eye would change the sense of the thought experiment using index finger and palm. As long as we're on the subject of scopes, I might as well mention focussing the ocular or eyepiece (same thing). The goal here is to focus the ocular, which is really just a magnifying glass, on the _crosshairs_ which are located just ahead of the ocular. To avoid the distraction of the objective's image, you can cover the objective with something translucent like maybe a sheet of
Kleenex. Screw the ocular out, away from the main body of the scope until the crosshairs go out of focus. Now screw it in until the crosshairs are just in focus and then turn it in a little bit more. This puts the crosshairs slightly nearer than infinity as far as your eyes can tell. Your eyes will appreciate not having to strain to focus on the crosshairs, especially if they're old eyes like mine. Even if you have young eyes, a long day of varmint shooting will strain your eyes if you've focussed your ocular by reversing the sense of the above procedure.
After you have focussed your ocular, you can set your parallax by the procedure delineated in the above paragraphs. This is quite often a more accurate way of setting parallax than setting by the yardage lines inscribed on the objective bell (on many brands those lines are approximate at best).
Warning! Snoozer follows!
Now can we calculate? Oh, goodie! On a short scope, the objective's focal length must be around 0.1 m considering that there is an erector lens in that tube also. The formula for the distances from a lens of the object and the image of that lens is:
O^-1 + I^-1 = F^-1
where:
O = distance from object to lens
I = distance from image to lens
F = focal length of lens
What I'd like to know is how far we'd have to bring the objective lens in if we shift the parallax correction from 50 m to 100 m. Moving the objective lens relative to the scope body makes no essential change in the value of the variable, O. So how far is the image from the lens when the target is at
50 m? 100 m? 150 m?
I(50) = [(F^-1)- (O^-1)]^-1 = [(.1^-1)-(50^-1)]^-1 = .1002 m
I(100) = [(.1^-1)-(100^-1)]^-1 = .1001 m
I(150) = [(.1^-1)-(150^-1)]^-1 = .10007 m
We can now see that we're talking very small parallax correction movements here and that furthermore, the corrective movement required for an increment in target distance decreases rapidly as the distance to the target increases.
So the answer to my question is, if you move the target from a 50 m distance to a 100 m distance, the objective must be moved .1002-.1001= .0001 m to correct the parallax. In Marekin terms, this is .004". That sounds about right to me considering that the graduations on an objective bell are fairly close together and the objective bell's thread is very fine. This also explains
why it is difficult for the scope manufacturer to put the parallax marks on
the bell in exactly the right place. All eyes are closed? Have a nice sleep!
[email protected] (John Bercovitz)
--------------------------------------------------------------------------------
From: [email protected] (John Bercovitz)
Subject: Re: Parallax adjustments on scopes(clarifications & corrections)
Organization: Lawrence Berkeley Laboratory
In article <[email protected]> [email protected] (Columbo Kotzar) writes:
##The above definition of parallax is correct for rifle scopes. The way parallax
##errors occur is that the primary image -I am used to dealing with real objects
##not virtual objects, silly me- is brought into focus on a plane that is not
##coincident with the plane of the reticle. When that occurs moving your eye
The images in a scope are real, not virtual, so you got it made!
##across the field of view results in the crosshairs moving relative to your
##target. The way this is corrected is by moving the objective element(s) to
##focus the image of your target on the same plane as the reticle. The movable
##objective element(s) actually do two things: first is focus the image of the
##object and second is fine tune where the focused image lies in the body of
##the scope.
I know you know the following, Geoff, but I think the above may be misread. You don't want to focus the scope with the objective. You focus the reticle with the ocular and then correct parallax with the objective.
Certainly if you have a scope adjusted correctly and your eyes don't have much accommodation left and you fool with the objective, the image will go out of focus, but that's a side effect.
##How much error are we talking about? I don't know at the moment but I have
##heard that 1/4 inch figure for scopes set for 100 yards when used at 50 and
##have seen about that amount when using one of the LER pistol scopes at 100 yds
#I hate to drag this out much further but there was one point that I overlooked
#and wanted to include. The magnitude of the error caused by parallax is a
#function of the scope magnification, at least it appears this way. The 1/4 inch
#number given above was for a 4X scope. As the scope magnification increases
#beyond about 9X parallax adjustment becomes important, so if you need 10X and
#greater magnifications you might want to look into a model that allows cor-
#recting for parallax (no pun intended). If you really only need 9X and less,
#you are probably shooting at something big enough that parallax errors are not
#important.
I tried to do a little calculating on this and got stumped at the point of figuring the effect of axial magnification of the ocular so I called Leupold and got their answer man, one Merwyn Webb. As I suspected, axial magnification doesn't really play a part in this. So it's all really rather straight forward:
According to Webb, regardless of scope magnification, if the objective's image
is .001" in front of or behind the reticle, the parallax error is 1" at 100 yards for the condition of the eye being at the extreme edge of the exit pupil, at least to the first order. (It also depends on the diameter of the exit pupil inasmuch as this sets the latitude you have in placement of your eye.) Since this is an angular problem, 1" at 100 yards is equivalent to 2" at 200 yards.
The reason it doesn't bother you in a low power scope is that this magnitude of
error is too small to see in a low power scope. I asked him if the focal length of the objective was around 0.1 m as I speculated in an earlier post and he said it was around that but it varied since the objective and erector often work together to set the focal length (ie, the erector often is not just a pure erector). Also, scopes designed for different purposes have different focal length objectives. If my figure of 0.1 m is correct, the image to reticle distance is .0001 m or .004" for a scope used at 50 but adjusted for 100 yards
(or vice-versa), as shown in an earlier post. This would correspond to a 4"
error at 100 yards or a 2" error at 50 yards if Mr. Webb is also correct. This sounds slightly high to me. I guess I'll just have to try this experiment and see what happens.
#Even if they are, slow down and place your eye along the scope axis
#and the error will go to zero.
Good advice. It's really not much harder to get your sighting eye on the axis of a scope than it is to get it on the axis of a peep sight.
[email protected] (John Bercovitz)
[ 03-02-2003: Message edited by: Dave King ]
As I understand it:
Focus adjusts the scope to the individual shooter's eye... this is a one time adjustment. (For geezers and wearers of prescription lenses this could be a multiple procedure event if new prescription arrive.) The purpose of this adjustment is to adjust the scope so that the image of the reticle (crosshairs) is properly aligned with the back of the shooters eye.
Parallax adjusts the target to the reticle (crosshair). The target image and the reticle must be on the same focal plane within the scope or there is room for apparent movement of the reticle on the target when the shooter'e eye moves (or is positioned differently at the scope).
Here are a few articles and bits of info on this subject.
From: [email protected] (John Bercovitz)
Subject: scope parallax, was Re: Colt M16A2 vs. Colt AR-15 Delta HBAR
Organization: Lawrence Berkeley Laboratory
There may be a modest amount of confusion out there on the subject of scope parallax. Parallax problems result from the image from the objective not being coincident with the crosshairs. (On high magnifications scopes, the objective is the big end of the scope; vice-versa for low power scopes; in either case it's the guzin end.) If the image is not coplanar with the crosshairs (that is the image is either in front of or behind the crosshairs), then putting your eye at different points behind the ocular causes the crosshairs to appear to be at different points on the target. (The ocular is the guzout end of the scope.) In fact, this is the basis of a test for parallax problems:
Set your scoped rifle on sand bags. Align the scope with the center of the target. Without touching the rifle, move your eye around behind the scope. Do the crosshairs appear to move on the target? If they do, the parallax is not set for the range of the target you are using.
So which way do we move the objective to correct parallax? First hold up the index finger of one hand in front of the palm of the other hand. (You don't have to actually DO it, this a thought experiment.) Let the index finger represent the crosshairs and the palm represent the image plane. If you move your head to the left, the finger moves to the right against the palm. So if your crosshairs move to the right on the target's image when you move your head to the left, the image plane must be further away than the
crosshairs. What's a mother to do? Why pull the image plane in a little by screwing the objective bell in so that the objective moves closer to you, of course. In this set up, the image is essentially tied to the objective so moving the objective 0.1 mm moves the image 0.1 mm. And no, the ocular
doesn't change this scenario any more than putting a weak loupe to your eye would change the sense of the thought experiment using index finger and palm. As long as we're on the subject of scopes, I might as well mention focussing the ocular or eyepiece (same thing). The goal here is to focus the ocular, which is really just a magnifying glass, on the _crosshairs_ which are located just ahead of the ocular. To avoid the distraction of the objective's image, you can cover the objective with something translucent like maybe a sheet of
Kleenex. Screw the ocular out, away from the main body of the scope until the crosshairs go out of focus. Now screw it in until the crosshairs are just in focus and then turn it in a little bit more. This puts the crosshairs slightly nearer than infinity as far as your eyes can tell. Your eyes will appreciate not having to strain to focus on the crosshairs, especially if they're old eyes like mine. Even if you have young eyes, a long day of varmint shooting will strain your eyes if you've focussed your ocular by reversing the sense of the above procedure.
After you have focussed your ocular, you can set your parallax by the procedure delineated in the above paragraphs. This is quite often a more accurate way of setting parallax than setting by the yardage lines inscribed on the objective bell (on many brands those lines are approximate at best).
Warning! Snoozer follows!
Now can we calculate? Oh, goodie! On a short scope, the objective's focal length must be around 0.1 m considering that there is an erector lens in that tube also. The formula for the distances from a lens of the object and the image of that lens is:
O^-1 + I^-1 = F^-1
where:
O = distance from object to lens
I = distance from image to lens
F = focal length of lens
What I'd like to know is how far we'd have to bring the objective lens in if we shift the parallax correction from 50 m to 100 m. Moving the objective lens relative to the scope body makes no essential change in the value of the variable, O. So how far is the image from the lens when the target is at
50 m? 100 m? 150 m?
I(50) = [(F^-1)- (O^-1)]^-1 = [(.1^-1)-(50^-1)]^-1 = .1002 m
I(100) = [(.1^-1)-(100^-1)]^-1 = .1001 m
I(150) = [(.1^-1)-(150^-1)]^-1 = .10007 m
We can now see that we're talking very small parallax correction movements here and that furthermore, the corrective movement required for an increment in target distance decreases rapidly as the distance to the target increases.
So the answer to my question is, if you move the target from a 50 m distance to a 100 m distance, the objective must be moved .1002-.1001= .0001 m to correct the parallax. In Marekin terms, this is .004". That sounds about right to me considering that the graduations on an objective bell are fairly close together and the objective bell's thread is very fine. This also explains
why it is difficult for the scope manufacturer to put the parallax marks on
the bell in exactly the right place. All eyes are closed? Have a nice sleep!
[email protected] (John Bercovitz)
--------------------------------------------------------------------------------
From: [email protected] (John Bercovitz)
Subject: Re: Parallax adjustments on scopes(clarifications & corrections)
Organization: Lawrence Berkeley Laboratory
In article <[email protected]> [email protected] (Columbo Kotzar) writes:
##The above definition of parallax is correct for rifle scopes. The way parallax
##errors occur is that the primary image -I am used to dealing with real objects
##not virtual objects, silly me- is brought into focus on a plane that is not
##coincident with the plane of the reticle. When that occurs moving your eye
The images in a scope are real, not virtual, so you got it made!
##across the field of view results in the crosshairs moving relative to your
##target. The way this is corrected is by moving the objective element(s) to
##focus the image of your target on the same plane as the reticle. The movable
##objective element(s) actually do two things: first is focus the image of the
##object and second is fine tune where the focused image lies in the body of
##the scope.
I know you know the following, Geoff, but I think the above may be misread. You don't want to focus the scope with the objective. You focus the reticle with the ocular and then correct parallax with the objective.
Certainly if you have a scope adjusted correctly and your eyes don't have much accommodation left and you fool with the objective, the image will go out of focus, but that's a side effect.
##How much error are we talking about? I don't know at the moment but I have
##heard that 1/4 inch figure for scopes set for 100 yards when used at 50 and
##have seen about that amount when using one of the LER pistol scopes at 100 yds
#I hate to drag this out much further but there was one point that I overlooked
#and wanted to include. The magnitude of the error caused by parallax is a
#function of the scope magnification, at least it appears this way. The 1/4 inch
#number given above was for a 4X scope. As the scope magnification increases
#beyond about 9X parallax adjustment becomes important, so if you need 10X and
#greater magnifications you might want to look into a model that allows cor-
#recting for parallax (no pun intended). If you really only need 9X and less,
#you are probably shooting at something big enough that parallax errors are not
#important.
I tried to do a little calculating on this and got stumped at the point of figuring the effect of axial magnification of the ocular so I called Leupold and got their answer man, one Merwyn Webb. As I suspected, axial magnification doesn't really play a part in this. So it's all really rather straight forward:
According to Webb, regardless of scope magnification, if the objective's image
is .001" in front of or behind the reticle, the parallax error is 1" at 100 yards for the condition of the eye being at the extreme edge of the exit pupil, at least to the first order. (It also depends on the diameter of the exit pupil inasmuch as this sets the latitude you have in placement of your eye.) Since this is an angular problem, 1" at 100 yards is equivalent to 2" at 200 yards.
The reason it doesn't bother you in a low power scope is that this magnitude of
error is too small to see in a low power scope. I asked him if the focal length of the objective was around 0.1 m as I speculated in an earlier post and he said it was around that but it varied since the objective and erector often work together to set the focal length (ie, the erector often is not just a pure erector). Also, scopes designed for different purposes have different focal length objectives. If my figure of 0.1 m is correct, the image to reticle distance is .0001 m or .004" for a scope used at 50 but adjusted for 100 yards
(or vice-versa), as shown in an earlier post. This would correspond to a 4"
error at 100 yards or a 2" error at 50 yards if Mr. Webb is also correct. This sounds slightly high to me. I guess I'll just have to try this experiment and see what happens.
#Even if they are, slow down and place your eye along the scope axis
#and the error will go to zero.
Good advice. It's really not much harder to get your sighting eye on the axis of a scope than it is to get it on the axis of a peep sight.
[email protected] (John Bercovitz)
[ 03-02-2003: Message edited by: Dave King ]
