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Optics and variables

Optics and variables

Optical variables


Objective Lens Size, Magnification, Exit Pupil and how they affect optical performance.


Optics banner



In this blog I will be discussing some of the mechanics behind rifle scopes.  While I will mention certain scopes as examples this is only because I am familiar with them – these mechanics are based on physics and no scope manufacturer can cheat them.


I’ll be discussing Magnification, Objective Lens Diameter and Exit Pupil, and how these three relate to each other and their effect on the observed image. 

As there will be a wide range of knowledge and experience between the readers of this blog, I’ll quickly explain a couple of terms –

  • Ocular lens – the lens that is closest to the shooters eye.
  • Objective lens – the lens that is closest to the target.  Can range from 20mm to 60mm in diameter
  • Parallax error – the error that occurs because the image and the crosshair are not in the same optical plane.  If the shooter were to move their head left, right, up or down then the image and the crosshairs appear to move relative to each other.
  • Light Transmission – the difference in the volume of light that enters and exits a single lens, usually expressed at a percentage.  As an example, if 100 units of light enter a lens and 98 units exit, that lens has a 98% light transmission.  This reduction is compounded as visible light passes through the numerous lenses in a rifle scope.

Magnification, Objective lens Diameter and Exit Pupil


Scope Magnification is the amount that the scope magnifies the target from its original size – An easy way to visualise this is that if something is 100m away and you have a x10 power scope, it will appear 10m away.  A x25 scope would make it appear 4m away.


Magnification (and its effects on other optical factors) featured in a previous blog – The Optical Triangle

To read about Magnification and it’s fit into the Optical Triangle, Click Here.


Front objective lens diameter is the diameter of the lens that is closest to the target, measured in millimetres. 


objective bell size 450



Exit Pupil and its Function


Exit Pupil is the diameter of the circular beam of light that exits from the ocular lens and hits the eye.  It is easily calculated – Exit Pupil is the objective lens diameter divided by the magnification.  A fixed ten power scope with a forty millimetre diameter objective bell (10×40) would have an Exit Pupil of four millimetres (40/10 = 4).  An eight point five to twenty five magnification scope with a fifty millimetre objective bell size (8.5-25×50) would have an Exit Pupil diameter of 2mm on its highest magnification (50/25 = 2) and a 5.9mm diameter Exit Pupil on its lowest magnification setting (50/8.5 = 5.9).


If the Exit Pupil is larger than the shooters pupil, then the image will appear ‘bright’, as the pupil could not take in any more light.  However, if the Exit Pupil is smaller than the pupil, then the image will appear darker through the scope than observed with the naked eye.  An example would be shooting at night – typically under restricted light conditions the pupil will dilate to roughly 7mm in diameter.  When using the above mentioned scope (8.5-25×50) on its highest power, with only a 2mm Exit Pupil, the image observed through the scope will be darker than that observed with the naked eye.  However, if the power were adjusted down to 10 or 12 power, the image would appear brighter.


Larger exit pupil 450


The other effect that Exit Pupil has on the image is ideal eye positioning for a clear image.  If you imagine the light that exits the ocular lens of the scope is a beam the diameter of the Exit Pupil, then the shooters pupil must be positioned within this beam to see the image clearly.  If you have a beam of light that is 2mm in diameter then it is difficult to get your eye in exactly the right position to get a clear image.  



 small exit pupil






But if the beam of light is 4mm in diameter, such as on a 10×40 scope, or 7mm in diameter such as on a 6×42, or 8mm in diameter like on a 4×32 scope, then the exact position of the eye behind the scope becomes less and less critical to get a clear image.  Quicker target acquisition allows for faster shots – an important factor when shooting fast moving or elusive game.



While larger Exit Pupils can mean more light and less critical head position for clear viewing, there is no free lunch – there are 3 draw backs from having larger exit pupil diameters.

  1. Large magnification scopes have smaller Exit Pupils than smaller magnification scopes.  Therefore, for the same objective bell diameter, having a larger Exit Pupil will mean having a smaller magnification.
  2. Increasing Exit Pupil diameter, for a fixed magnification, will require increasing the objective bell diameter.  While the image may be easier to see, the firearm will need to be fitted with higher rings so the objective bell on the scope does not touch the barrel.  This may require the shooter to place their head in an unnatural position to see through the scope clearly.
  3. Large Exit Pupils mean less critical head position for viewing – the bigger the Exit Pupil the further the eye position can be moved up, down, left or right and still maintain a clear view of the image.  The further the shooter can move their head away from the centre of the ideal viewing position, the more parallax error they will have.


How important is Exit Pupil?


Exit Pupil is a function of magnification and objective lens size 


So with larger magnification scopes, one could be mistaken to think that they need as large objective bell diameter as they can buy to get a larger Exit Pupil to reduce the loss of available light. For example, going from a 6-18×40 to a 6-18×50 does increase the Exit Pupil diameter by 20%, which would have an effect on the brightness of the image.  However, there are two other factors that may have a more profound effect on the observed image brightness – light transmission and the number of lenses a scope contains.  These will be covered in a later blog.


In summary, choosing the best scope is about deciding on what is important for your particular style of shooting.  There are many features of scope manufacture in addition to those covered here, but just like the optical triangle, the physics behind Magnification, Objective Lens Diameter and Exit Pupil is always going to be a balancing act to get the best performing scope for a particular rifle platform.  


 – Zaine Beaton


If you wish to comment or provide feedback on Zaine’s blog you can contact him via the email address – zaine@beatonfirearm.onpressidium.com

This email address is for contacting Zaine in direct relation to blog articles only – not for general correspondence or sales inquiries.  For sale inquiries, please visit our Contact Us page

Please keep in mind that these are Zaine’s personal comments – they are not a reflection of the opinions of any other staff or directors of Beaton Firearms.



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