SCOPES AND PEEP SIGHTS

 1

Lens power - Dioptres and Magnification

There is a lot of confusion here.  Scope lenses are sometimes shown as having a power in dioptres (eg +0.75 or just 0.75), and sometimes as magnification (eg 6x), but the magnification number is almost meaningless.

The simple fact is that you cannot convert dioptres to magnification without knowing the eye-to-lens distance, and this varies greatly not only between archers, but between set-ups. You can easily see this by moving your scope backwards and forwards and noticing how the size of the image changes. Specialty Products say that their lens powers all refer to a peep-to-lens distance of 34 inches, but even this is open to some doubt if you look at the figures in Section 2.  

Many archery manufacturers appear to use the rule of thumb that magnification = dioptres x 8, but this wildly misleading and only the dioptre value itself is reliable as it doesn't change however the lens is used.  When dealing with different manufacturers, you can't even be sure which lens is the more powerful if all you know is the so-called magnification.  For example, I have a so-called 2x lens which is almost identical in power to another manufacturer's 4x.  The fact is, there is no standard, so the archer must beware, and as usual, try out any scope if at all possible, before buying it.

Some Optical Theory (if you want it)

The dioptre (US: diopter) value of a lens = 1/ (Focal Length in metres). So a +0.5 dioptre lens has a focal length of +1/0.5 = +2.0 metres. The '+' sign means that the lens is a converging lens and will cast a real image on a suitable screen: all scope lenses are converging lenses, so the '+' is often omitted. Peep lenses are diverging lenses and have a negative dioptre value. Together, the +ve and -ve lenses form a crude Galilean telescope.   

It is easy to find out the focal length of a lens by measuring the distance at which the lens produces a sharp image of a distant light source on a screen of some sort, such as a sheet of paper (distant in this case need only mean more than about 10 metres away).  The sun is an obvious choice for a light source, but be careful you don't set fire to anything as the image can get pretty hot, even with the comparatively weak lenses used for scopes.  The distance from the lens to the image is the focal length.

The magnification of a scope lens is given by the formula:

M = 1/(1-d*D)

M = Magnification
d = distance from eye to lens in metres
D = Dioptre value of the lens

So, for example if the lens is .5 dioptre (a so-called x4) and the eye to lens distance is 30 inches (0.76 metres) :

M=1/(1-0.76*0.5)=1.62

And yes, 1.62 (or, using a slightly different convention, 2.62) is the correct answer not somewhere around 4.00, as you might expect. 

Magnifications for the common lens powers at representative distances are as follows:       

There are several things to note here. 

First, none of the true magnifications bear much resemblance to the quoted power and it is therefore easy to see how a manufacturer could quote almost any number for any lens and be equally (in)correct.

Secondly, small changes in sight extension can have a big  effect on magnification, and in the commonest range - about 30 to 35 inches - there is potential for a lot of overlap, especially in the lower power lenses.

Finally notice that the higher magnifications cannot be used with long eye-to-scope distances. In fact no lens can be used as a scope if the eye-to-scope distance is greater than or equal to its focal length.  In theory, its image becomes infinitely big (ie can't exist).  In practice what happens is that it becomes impossibly blurred and it is essential to use a clarifier lens (when a whole new set of equations apply which we don't need to go into here).

3

 What power lens should I use?

More powerful lenses give a bigger image, but it is more blurred, less steady and darker. It also covers less of the target, which can make finding the spot (or at least, the right spot!) very difficult.  If you really want to see what I mean, try shooting an IFAA animal round with a lens of 1.00 dioptre or more. How much these factors matter to you personally depends on all sorts of things, including how good your eyes are in the first place and whether you wear glasses or not (in general, glasses wearers will find the higher powers difficult to use). Standard lenses are made in steps of 0.25 dioptres and, in practice, only five values are usable in scopes A rule-of-thumb guide is as follows:

Does size matter?

Optically, not much. Bigger scopes collect a little more light (including more glare and reflections) and have a slightly bigger field of view. Try a bigger scope if you use a more powerful lens, but make sure you can get the left/right extension you need and remember that half the scope may disappear behind the riser at full draw.  

5

Transparent and opaque bodies

Transparent scope bodies give the illusion of a brighter image, but they can do nothing to increase the mount of light that comes from the target - and that is the only light that you want to see. All transparent bodies do is increase the amount of reflection and glare, which is light you certainly don't want to see.  The idea that a lens in a transparent body can somehow use light that comes in from the edges to boost the image is nonsense - unless optics has changed an awful lot since I studied it at university.    If you need a transparent body to see your sight ring or bubble properly, get a better designed scope.  If you have a transparent scope, I strongly suggest covering it with insulating tape or something similar to make it opaque.

 The Beiter Scope in one of its many different configurations.

In its black bodied version, probably the best all-round scope on the market. High quality and offering well over 200 possible configurations of lens, pin, aperture, shield and bubble.

More details on the Beiter website  

Does the shape of the lens matter?

In practice, only two cross-sectional shapes are used in archery scopes: 

Meniscus lenses are often cheaper as they can be made from mass-produced plastic spectacle lens blanks, although the better ones are purpose made from optical glass.  Plano-convex lenses tend to be more expensive and are almost always glass.

In theory, plano-convex lenses are the best, because they are less prone to reflection and are easier to machine precisely.  In practice, provided the lens is coated, shape isn't very important: it is overall quality that counts.

The Optical Centre

Lenses form their image centred on a point known as their optical centre.  Ideally, this should be the same as the physical centre of the lens in all three dimensions.  However, if you hold your scope out at arm's length and rotate it, you may see the image moving in a circle around the physical centre.  If it does, then the optical centre of the lens is not at the physical centre.  This is quite common even in the more expansive lenses and I strongly suggest you try the test - you may be surprised at how much movement there is.  

The practical implication is that if the imperfect lens turns in its mount, or if you take it out to clean it and replace it in a different position, your sight mark will change as the image (which is what you actually aim at) will be in a different place.  To avoid this problem, mark the edge of the lens with a permanent marker pen, or note the position of any mark already there, align it with something on the body and make sure it is always in the same place.  It is a good idea to do this anyway, even if you think your lens is perfect - I certainly do.  

A similar effect takes place if you tilt your scope to a different angle from one shot to another.  Scopes produce what is called a 'virtual' image, which means an image that you can see only when looking through the lens - it is not 'real' in the sense that it cannot be projected onto a screen.  This image appears to be formed in front of the lens and will appear to move up and down as you tilt the lens, if the optical centre is not at the physical centre, or if it is not exactly aligned with the threaded rod attaching the scope to the sight.  If you tilt the scope forward the image will be lower and so will your arrows (and vice versa)

In practice this means that you should lock your scope solidly, even if this means a compromise at the longest and shortest distances, and you should check it frequently.  If you must adjust your windage by rotating your scope - not a good idea -, then be very sure to always return it to the same degree of tilt.  

As usual I recommend that you experiment.  You will find that on some scopes this is far from a theoretical niggle:  it this is a significant source of potential error, and one that is seldom suspected by the archer.

8

 Are coated lenses worth the extra money?

Yes. A good multi-layer coating may double the price of the lens, but it will give a brighter image and cut out 70% of the glare and reflection at the same time.

9

Peep sight sizes

Ordinary peep sights (ie those without lenses) must perform two functions: they must allow accurate line up with the scope, and they must clarify the image, which they do by cutting out the less focused rays of light, while allowing enough light through to be able to see clearly.

The first part is easy. Just make sure the hole is big enough for you to see the entire diameter of the scope when you aim, so you can centre it accurately. However, clarifying the image is a compromise, like most things in archery. The smaller the hole, the less blurred the image will be, but it will also be darker and more prone to flare if the sun strikes across it. 

The best way of getting the  hole size that suits you is to buy a plain aluminium peep with the smallest hole you can get, then enlarge it in small steps by turning a needle-file gently in the hole until it is the size you want. If necessary, cover any bright metal with matte black paint.

Incidentally, the size of peep does not make any difference to the true magnification, although a large peep can give an illusion of higher power, because the image is more blurred and therefore looks bigger.

10

Clarifier and magnifier peeps

The difference between a clarifier peep and a magnifier peep is simply one of degree: both have a lens (see footnote above), but it is stronger in the so-called magnifying peeps. Optically, both work well and you may not be able to use the higher powers of scope without them. However there can be disadvantages. First, although the target will be clearer, the scope itself may be much less clear. If you use a large sight ring this may not matter, but if you use something like a dot or cross-hair it can vanish completely at full draw - along with your bubble. Secondly, if your peep lens gets dirty or collects a drop of rain it is virtually impossible to clean it in the field. Finally, these peeps are very prone to flare and can be a nightmare in bright sun. All in all, as you will have gathered, I don't favour clarifiers or magnifiers - but that's just me.