Parallax vs Focus

Discussion in 'Long Range Scopes and Other Optics' started by Dave King, Mar 2, 2003.

  1. Dave King

    Dave King Well-Known Member

    May 3, 2001
    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: (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
    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! (John Bercovitz)


    From: (John Bercovitz)
    Subject: Re: Parallax adjustments on scopes(clarifications & corrections)
    Organization: Lawrence Berkeley Laboratory

    In article <> (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! :cool:

    ##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

    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. (John Bercovitz)

    [ 03-02-2003: Message edited by: Dave King ]
  2. Brent

    Brent Well-Known Member

    Jun 12, 2001
    Thanks Dave,

    I like the last sentance there, it's so true, not hard to do at all if you back your eye off the ocular a bit.

    I like the finger in front of the hand explanation. Makes for an easy explanation to someone, and helps you decide wich direction to correct too. [​IMG]

  3. Guest

    Guest Guest

    [ 07-12-2003: Message edited by: S1 ]
  4. CatShooter

    CatShooter Well-Known Member

    May 8, 2001
    Good morning Dave.

    I received an e-mail this morning from one of your readers about this thread, asking, in effect, "What the hell is that?"

    The text you copied is a bit confusing... it is filled with a mix of over-scientific terms like "coplanar" that would be out of place in a research paper on the subject, and words like "coincident" which means nothing to a shooter... and these are mixed with cutesy phrases like "guzin" and guzout" ;(

    But then again, what would one expect from something that originated from UC "Berkeley".

    I wrote the following a few months ago for a friend, and I'm putting here (in total), cuz I think it is written for real people, and might throw some light on the subject.
    (HA!, I made a pun on purpose [​IMG] ).

    It drew some flack from a few whimps that would love to have ME in their sights, but it is right on, and you can take it to the bank!


    OK... here goes (Whew, this is gonna be a long one).

    There are several things that go on inside a scope, and in the eyes at the same time.

    Some of them workie against each other.

    But some terminology first... and we'll leave out lenses that are there to correct some optical or color errors, but don't have anything to do with image forming.

    We'll start at the front of it all, and work back.

    1 - The "Object"... the thing that you are looking (shooting) at.

    2 - The "Objective". The front lens is called the "Objective"... it forms the first image of the "object" we are looking at (that why they call it the Objective [​IMG]

    It is the lens that "captures" all the light, that is solely responsible for the image quality of the scope... if it is poor, you can't fix the poor image later.

    This lens is usually made of two different types of glasses (called "elements") sandwiched together, and is called an "Achromat".

    The Achromat is fully color corrected for blue and green. The red wavelengths are partially corrected, but have what is called "residual color errors".

    This is the normal type of objective used in shooting and spotting scopes.
    In quality, they can vary from badd, through sorta OK, to pretty damn good.

    If one of the elements is made of an "ED" glass, or a "Fluorite" (CaF) glass, the two element lens can be very good to friggin' outstanding.

    In some instances, objective lenses are made of three elements, and all three colors (blue, green, and red) are completely corrected. This type of lens is called an "Apochromat", and this is the finest lens that can be bought. The best of these can also have "ED" glass, or Fluorite as one of the elements.

    3 - The "First image plane". The Objective focuses the light to make an image of the subject, just like a camera lens. This image is upside down, and right/left reversed. This is the first image plane, but NOT the "First image plane" that is talked about when shooters talk about reticles.

    4 - The "Erector lens"... (if it is a group of lenses, it is called the "Erector cell"). Because the first image is upside down/wrong way around, we (as shooters) can't use it... so we flip it around with a simple optical group called the "erector cell".
    This cell gives us a new image that is right way around, called the second image plane. Moving this cell causes this second image plane to move... so micrometer spindles are put against the cell, to get elevation and windage adjustments.

    5 - The "Second image plane". This is the second real image plane in the scope, and this is the image plane that shooters call the "First image plane" when talking about reticles. In a fixed power scope, or in a variable with a "First image plane reticle", the reticle would be placed in this image plane.

    This is where Premier Reticle puts those magical "Gen II" reticles.

    6 - The "Zoom group". In a variable scope with standard (non-magnifying) reticle, the zoom group of optics would follow #5. This group of lenses can change the size of the image plane in #5 and then form a new (third) image plane behind it.

    7 - The "Third image plane" In variable power scopes, this is the plane that the reticle is placed in. By being here, it allows the image to change sizes, but the reticle to stay the same size. In the context of reticles, this is the image plane that is referred to as the "second image plane"

    8 - The "Eyepiece". This optical group is like a jewelers loupe. Is is (or should be) a super fine magnifier. It's only job in the whole world, is to focus on the reticle.

    Let me repeat that for those that live in Rio Linda...


    It CANNOT adjust, or compensate, or do anything else when things look bad in the scope, or when you can't hit the target... and to try to make the eyepiece correct for parallax, is sheer folly at best, and raw stupidity at worst.

    If you expect it to do anything else, then stop wasting your time with long-range shooting, cuz you are never gonna make it past mediocre... and take up golf!!

    OK... now that you know what the insides are like... lets move on. We'll use the zoom scope for our examples. cuz if you can understand the zoom, then the fixed is a walk in the park.

    In the scope that is set for infinity range, the object forms an image behind the objective (the first image plane)... the erector cell "sees" that image, and flips it over and makes a NEW image plane (the Second image plane). The zoom group adjusts the size of this image plane, and makes a NEW image plane (the Third image plane) that is the desired size.
    There is a reticle placed in this last image plane, and the eyepiece focuses on the reticle AND the image at the same time.

    When things are good, that's how the scope workie!


    But... now the booger falls into the soup... IF the third image plane and the reticle are not exactly, (and I mean EX-ACT-LY) in the same place, then your eye cannot see them LOCKED together as one picture.

    It sees them as two separate things, and the eye can look at each separately, and the eye can also look AROUND one to see the other.


    Lenses are normally measured in metrics (aka Millimeters). Not because the Europeans wanted it the metric system 20 years ago, but because optical strings and chains of lenses (like scopes) are really a string of numbers.

    There are constant ratios of "this divided by that's" that give image sizes, "F-ratios", and image locations. It's so damn easy to do the engineering using a 10 based system that the optical guys were using the metric system way back in the 1800's.

    The objective has a "Focal length"... this is the distance behind the lens that the first image plane falls when making an image if a subject that is at infinity (or very damn far away).

    If the objective has a focal length of 100mm, then the image of that 1000 yd target is 100mm behind it.

    But the problem with geometric optics (which is what we are dealing with here), is that they follow the laws of geometry...
    ... and optics make triangles like rabbits make babies.
    AND... in an optical chain, when you change one thing, one angle, one ANYTHING, everything else follows along and changes BASED on the ratios involved at THAT stage.

    If we take that same target, and move it to 100 yds, the image in the scope moves BACKWARDS, going further into the scope. Not by much, but it doesn't take much, cuz we're dealing with very small distances inside the scope, and very high magnifications.

    How far the image moves back, and what it's new position is, is predictable by the mathematical ratios of the angles formed by the subject and the first image...

    ...OR (for us dummies that lost our slip sticks) by the ratio of the distances to the Target and the focal length, multiplied by the focal length. then ADDED to the focal length.

    The target is at 100 yds (91440mm), the focal length of the objective is 100, so the displacement is 1/914 x 100, which means that the first image is now at ~100.1mm. Hmmm only .1mm, that doesn't seem like much.

    Read the following paragraph twice...

    In a 1x scope, 0.1mm would mean nothing... but this displacement is repeated throughout the chain, AND if any of the optical groups change the image ratio, then the displacement (aka ERROR) is changed in direct proportion to the increase in magnification.

    So in a 3x scope, it would be .3mm, and in a 10x scope, it would be 1mm, and in a 30 power scope, the image would be 3mm behind the reticle. This means that if you have a variable scope, and things look good at 3x, they may NOT look so good at 12x. Set your parallax corrections at high power.

    Now, you should have seen a pattern in this last paragraph.

    With the same error in the objective (scope focused at 1000, and target at 100), the parallax INCREASES WITH MAGNIFICATION... got it? If not, READ IT TWO MORE TIMES!!

    OK... now, if we do the same math for closer distances, like 50 yds, and 25 yds we will see that the error gets really big, so that with a target at 50 yards, and the scope set at 35 or 65 yds, the parallax makes the combination un-usable.


    Parallax is... when the image of the target, and the reticle are NOT in exactly the same plane, and by moving the eye up and down... or side to side, either the target OR the reticle appears to move in relation to the other.

    You might see the target move and the reticle stay still, or you might see the target stay still and the reticle move over it... both are exactly the same, and which you see, is only a matter of your OWN perception.

    It is impossible to have parallax while moving up and down, but not have it when you are moving side to side.

    If you think that is what you have, you have other problems... either you are moving the rifle, or you have eye problems.



    This is the only way to do it...

    First, screw the eyepiece out (CCW) all the way, until it stops.

    If you wear glasses, put them on.

    Hold the scope up and look OVER the scope at the sky, and relax your eyes.

    Then move the scope in front of your eye.

    The reticle should look fuzzy

    Turn the eyepiece in 1/2 turn, and do the same thing again. You will have to do for a while before the reticle starts to look better. When you start getting close, then turn the eyepiece 1/4 turn each time.

    Do this until the reticle is fully sharp and fully BLACK immediately when you look through the scope.

    Than back off a turn and do it again to make sure you are in the same place.

    Then LOCK the ring on the eyepiece, and leave it alone forever!


    Set the scope down on something sold, where it can see something at a long distance... half a mile of longer is good.

    It can be on the rifle, and rested in sand bags at the range... but pick something at least 1000 yds away... even further if possible.

    If the scope has an "AO" Adjustable objective, then set it for infinity, and look at the distant object, and move your head from one side to the other, or up and down if you prefer.

    If the reticle seems to move, there is parallax.

    Change the distance setting and try again... if you are very careful, you can move your eye, and adjust the distance at the same time, seeing which direction gets better.

    With front objective adjustments, you can turn them either way without worry... BUT with side adjustment scopes, like the MK4-M3, the M3-LR, or the other LR family of scopes, the adjustment must ALWAYS be made from the infinity end of the dial. Turn the adjustment all the way until it stops (past infinity), and then start turning it in a little at a time, until there is no parallax.
    If you "overshoot" the proper setting, you can't just turn back a little, you must go back to stop at the end of the dial, and start over again.

    While "AO"s dials are locked in place, and if the indicated distance doesn't match the real distance, there's nothing you can do about it...
    ... the side focus dials are not locked in place.

    Once you have found the setting for infinity on the side focus models, then (CAREFULLY) loosen the screws, and set the dial so that little sideways infinity symbol is lined up with the hash mark, so it is calibrated. You can also make little marks or put on a paper tape for other ranges instead of using the round dots that don't match any range.

    Now you can set it to infinity, but remember that you MUST turn the dial all the way past infinity to the stop, EVERY TIME before going from a close range to a longer range.

    If you are set for 500 yds, you can go directly to 100 yds, but if you are set for 100 and want to set it to 500, you MUST go all the way back to the stop, and then go to 500

    This is because there is a fair amount of backlash (aka SLOP) in this wheel linkage to the focusing cell, so you can set it only from one direction to make sure the slop is always on one side.
    The other problem with it is, even if you decided that you wanted to calibrate from the other end... the recoil will push the cell back. SO you must ALWAYS set these dials from the infinity end of their scales.

    To make it easy to not have to remember... I always start from the end stop, when I change range, no matter which direction I'm going in... it adds about 0.023 seconds!

    Now... you gots a friend that says to set up a scope a different way???...
    ... he don't know doodly-squat about scopes.

    The guy at the range said to do it a different way... he don't know shit either.

    Some guy who's in the Marines says something different... he don't know crapola!

    You got a friend that shoots benchrest and does it different... he doesn't know shit about optics either.

    This is the way, the only way, there is no other way.

    ... as Rush Limbaugh would say... this is from GOD-da [​IMG].


    So, Dave... there are two focus' in the scope. One for the eye, that should be set once, and one for the target that should be adjusted often.

    In a perfect world, manufacturers would ALL call the eyepiece adjustment "FOCUS", and call the objective adjustment "PARALLAX"... but many companies call the the target adjustment "focus" so there will never be an end to this.

    CatShooter [​IMG] [​IMG]

    [ 03-08-2003: Message edited by: CatShooter ]
  5. Darryl Cassel

    Darryl Cassel Well-Known Member

    May 7, 2001

    That was the BEST information on making scope adjustments I believe I have ever read.
    Great for us common folks

    Good job.

    Did you get the info from the range that we spoke about?

    Darryl Cassel
  6. Dave King

    Dave King Well-Known Member

    May 3, 2001

    Good to hear from you again and thanks for the clarification(s).

    Eyepiece focus has never been a problem for me, I've never heard it confused with parallax. It's that pesky Parallax (aka Focus) knob/dial that sticks in my craw. As long as that target image dosen't move in relation to the reticle I'm a happy camper, call it focus (okay) or parallax (better) either way is acceptable (somewhat... I'm trying to set a terminology standard here).

    An Update on my toys: George Gardner should have a 50 BMG ready for me in a few weeks.... [​IMG] [​IMG] [​IMG] McMillan RPRB single shot, Schneider (?), modified M14 bipod, McMillan stock, NightForce 5.5x22. Now I'll be able to play like the big boys.

    (Good cat shooting to ya!)
  7. Darryl Cassel

    Darryl Cassel Well-Known Member

    May 7, 2001
    Hello Again

    1 st Match May 3 & 4
    2 nd Match May 17 and 18

    Hope to see you there

  8. Holmes

    Holmes Well-Known Member

    Feb 26, 2002
    Thank you kindly, Catshooter.

    Cut, pasted, and archived for reference.

    This site has become my #1 source for new knowledge.

    Thanks to all.

  9. CatShooter

    CatShooter Well-Known Member

    May 8, 2001

    Thanks. I'm shooting a Sniper's match in W.Va in the 17th/18th, and for the first one, I may not be ready, but I'll make the one after that if I can.

    BTW... do you know the altitude (above sea-level) of the Williamsport range?

    Eyepiece focus has never been a problem for me, I've never heard it confused with parallax.

    There is the belief by many (and I've heard it from military shooters also), that you can correct parallax by using the eyepiece. Very badd juju.

    You live near the match... come to the Sniper's match on the 17th/18th. It's going to be a blast (HA!).

    Me and my spotter are bringing two 50-BMGs (AR-50's) for informal shooting after the match, and someone is bringing a Barrett 82A. I have made a spigot adaptor thingie for the AR-50 that allows the use of either the Parker-Hale or the M14 (unmodified). They both work very well.

    I'm shootin 830 grain M48's that are better than the forth of July... trace for over two miles, and a big detonation and 8 foot cloud of smoke on contact...

    ... "Come on down!" [​IMG] [​IMG]


    [ 03-07-2003: Message edited by: CatShooter ]
  10. Darryl Cassel

    Darryl Cassel Well-Known Member

    May 7, 2001

    900 feet.

  11. Ian M

    Ian M Well-Known Member

    May 3, 2001
    An engineer who can talk "people-talk"... you are a what this world needs more of. Thanks for a great batch of info, easy to read and understand.

    I have several boxes of Barnes .50 cal projectiles, they look like copper toothpicks. Won't work in in-lines, maybe we should get together and launch the suckers. I could pull eight or ten .308 cartridges to get us some powder for each .50, you just bring the new GardnerGun and some primed brass [​IMG]
  12. CatShooter

    CatShooter Well-Known Member

    May 8, 2001
    Hi Darrel...

    Thanks... I wrote it for a friend in a fashion that it could be understood by anyone (even a G... Gi... Gir... Girl! [​IMG] )

    As to the information... Yes (I think [​IMG] )

    I have boxes of mail from the last few months that I have to go through, but I do have a memory of the letter getting here.
    I plan to send in my money, grab a stick, drive the eleventeen hundred miles, and let you guys embarrass the hell out of me [​IMG]

    When is the first weekend that it starts?


    [ 03-07-2003: Message edited by: CatShooter ]
  13. CatShooter

    CatShooter Well-Known Member

    May 8, 2001
    [ 03-08-2003: Message edited by: CatShooter ]
  14. Dave King

    Dave King Well-Known Member

    May 3, 2001