By Pierre van der Walt

The Human Eye

The human eye, with its restrictions and abilities, forms an indispensable part of the riflescope as a sighting system. Optical engineers are compelled to take this into consideration when designing a riflescope, thereby adapting it to the human eye.

It is, therefore, important to grasp the fundamental functioning and limitations of the eye in order to understand the workings of a riflescope.

The human eye can roughly be described as a spherical organ with a 25mm diameter. It consists of a transparent section known as the cornea. Behind the cornea one finds an aqueous-filled anterior chamber, and then the iris which surrounds the lens perimeter and also slightly overlaps it. At the back of the eye there is a reasonably large chamber known as the vitreous body. The rear three-quarters of the inside of the eye consists of a layer of light-sensitive receptors known as the retina. Insofar as riflescope use is concerned, the most important sections of the eye are the cornea, lens and the retina.

Light is necessary for sight. Light rays reflected by any object pass through the cornea and then through the lens to focus on the retina. The image on the retina is then transmitted through the optic nerve to the brain where awareness of the image takes place. The amount of light that can penetrate the eye is controlled by the diameter of the pupil. Pupil diameter is controlled by the involuntary muscles of the iris. In bad light the pupil enlarges and in good light it contracts.

The maximum diameter to which the pupil can expand is about 0.275” (7mm), and then only in pitch darkness. As soon as light passes through the pupil the lens (which has a biconvex shape) is refracted. The refraction focuses the light rays on the retina.


Once light rays have passed through the scope lens and having been refracted by the lens glass, it moves through the vitreous body and focuses the image on the eye’s retina. The best focus occurs on a point which is in line with the visual axis of the eye. This point is referred to as the fovea. The focus at other areas of the retina is not as crisp as at the fovea, mainly because of the angle with which the incoming light rays fall on the retina and the imperfect focal points thereof. Light refracted by having passed through a convex lens furnishes a poor image at high magnification. This occurs because the light rays pass through the lens at different points and a complete image does not form at exactly the same horizontal distance from the lens. The centre of the lens has the longest focal length. The focal lengths of surrounding lens areas shorten in direct relation to the curves of the surrounding lens surface. This problematic phenomenon is known as aberration.

Several different types of aberration exist, but are not of any importance for purposes hereof. Chester Moore Hall (1703 – 1771) solved the problem created by aberration by combining crown glass (glass not containing lead or iron) and flint glass (which has different refracting indexes) in a single lens assembly consisting of a convex crown grass lens and a concave flint glass. This enabled him to focus the rays of white light on a single focal point with virtually no separation of the different rays which make up white light.

Ballistic Turrets

These are turrets on riflescopes that offer multiple zero options. In other words, the hunter can zero across various known distances. Say at 100 yards, 200 yards and 350 yards, he can simply dial the range in and shoot with less or no holdover depending on the exact range to the target.

Erector & Field Lenses

One of the most important differences between astronomical and riflescopes is that the latter sports erector lenses in order to furnish an upright image.

Apart from objective, ocular and erector lenses, modern riflescopes also contain field lenses. These lenses influence the route that light rays take through a riflescope and determine the field of view.

Light rays passing through the objective lens group are bent by the convex shape, thereby resulting in an inverted image. Because this group consists of different types of glass, aberrations are corrected and all light rays focus at the same point.

The light then passes through the erector group which turns the image upright. The erector lenses once again have a focal point where the image is in perfect focus. From here the light passes through the ocular lens group into the eye.

In order to have any use as a sight, a riflescope must have sighting mechanism. In modern riflescopes it is the reticules or crosshairs, dot, or whatever reference points has been used.

The reticules must at all times be clearly visible to the shot. There are only two places inside a riflescope where a sharply focused image of the target at all times exists and those are the focal points of the objective and erector lens groups. These focal points are the only places where reticules can be installed in such a manner that both target and reticules are well focused and appear as clear images. Once the light has passed through all the riflescope lenses it reaches a point where the shot can see everything that has been reflected on the objective lens. This point is at the focal length of the ocular lens group, and the distance between this point and the ocular lens group is known as eye relief. Theoretically, this means that there is only one critical point behind a riflescope where a shot can place his eye and see a complete and clear image. In practice, aberration comes to the aid of the shot in this regard because all the light rays exiting from the ocular lens do not have the exact focal length. It is possible to move the eye slightly to the front or the rear of the focal plane and still see a satisfying image. This contributes to fast eye alignment and reduces aiming time, both of which are very important to the hunter.

Eye Relief

Eye relief is the distance at which you can see the full image view through the scope and determines how far behind the riflescope’s ocular (rear) lens the hunter will place his eye for optimum visibility. If you move your eye nearer or further back from the objective (rear) lens, the field of view begins to constrict. Insufficient (short) eye relief will force the hunter to hold his eye close to the riflescope and he can then be hurt when recoil slams the riflescope back into his face. Long eye relief enables the hunter to safely fire hard-recoiling riflescopes without risk of injury. Eye relief varies as magnification on a riflescope is adjusted. The higher one cranks the magnification up, the shorter the eye relief becomes.

The average eye relief for centerfire caliber riflescopes is about 3” (75mm). Riflescopes designed for big bore rifles normally have eye relief varying between 3.5” – 5” (90 – 127mm), and rimfire rifle riflescopes have only 2” (50mm).

Exit Pupil

The extent to which the light rays that fall on a riflescope’s objective lens can be concentrated depends on riflescope magnification, because the riflescope’s exit pupil is determined by dividing the objective lens diameter by the magnification of the riflescope.

A riflescope with a 4x magnification and an objective lens diameter of 40mm has a 10mm exit pupil (40 ÷ 4 = 10mm). In order to fully utilize a riflescope’s objective lens diameter, its resolving power must be sufficient to create an exit pupil with the exact diameter of the human pupil under the prevailing light conditions. To illustrate: A riflescope with a 40mm objective lens requires 7x – 8x magnification to fully utilize the 40mm of lens diameter, because in early morning and late afternoon light the human pupil has a diameter of 0.197”-0.236” (5 – 6 mm). For example: (40mm lens ÷ 7x magnification = 5,7mm exit pupil and 40 ÷ 8 = 5mm).
Optical tests conducted by the Americans during the Second World War established that the human eye can contract to ±0.1” (±2,5mm) in bright light. At dusk, with a light intensity of one candlelight (stated as a candela) the human pupil diameter is 0.197” (5mm).

Suppose you are hunting on a very clear day in bright sunshine and will most likely have a pupil diameter of ±.12” (3mm) and intend using a 4x magnification riflescope. The objective lens diameter will only have to be 0.472” (12mm – 3mm exit pupil x 4 magnification = 12mm). If the objective lens diameter is any larger it will pick up reflections and images under these conditions that the human pupil is unable to absorb.
But light conditions vary, and sometimes the light is poor. Under such conditions your pupil will expand to, say 0.236” (6mm). A 12mm objective lens will absorb insufficient light under such conditions to allow optimum vision, and such a riflescope will be useless, the reason being that the eye pupil of 6mm requires a 6mm exit pupil and a 24mm objective lens (6mm pupil diameter x 4 magnification = 24mm objective lens).
It is for the abovementioned reason that no modern riflescope sports a 12mm objective lens diameter. Another reason exists. A larger diameter exit pupil enables a shot to align his eye faster and easier, because his eye does not have to be exactly behind the centre of the riflescope’s ocular lens. The drawback of unused image whilst using large objective lenses is a small price to pay for the added convenience of better vision and ease of alignment.

Very view advantages in optics come free, and the convenience of a large exit pupil on a riflescope holds the disadvantage of parallax. More about that later.

Field of View

If a hunter holds his eye at the correct eye relief distance from the ocular lens, a cone of sight stretches from the eye pupil to the rim of the ocular lens. This cone forms an angle stretching from the lens rim on the one to the eye and back to the opposite side of the lens rim. This angle is the maximum angle that can be seen through the particular riflescope and is known as the field of view. Suppose a riflescope with a 6x magnification has a field of view of 24°. The visible field at 100 metres will be approximately 37 metres. Because this distance is magnified 6x (reduced) by the particular riflescope, one must divide the distance (37 metres) by 6x. The actual field of view at 100m then is 6,16m (20.2ft). Although it sounds logical to express a riflescope’s field of view in degrees, valid for all distances, most manufacturers express the field of view as one distance at another, for example, 12,8 metres at 100 metres. This system is more concrete and easier to grasp. It means that the shot will see an area of 12,8 m diameter at a distance of 100 metres. At 50 metres he will see 6,4m (half) and at 200 metres 25,6 metres (double).

A riflescope’s field of vision can be widened in three ways:

  • The first is to reduce eye relief. The problem created by this method is that the aiming eye must be held to near to the ocular bell. Recoil can then cause injury when the scope is slammed into the shooter’s face.
  • Another approach is to reduce magnification.
  • The third and easiest solution is to simply increase ocular lens (rear lens) diameter.

Focal Plane & Reticule Position

Where reticules are placed in a riflescope affects the way in which they are perceived by the hunter. A reticule placed in front of the erector assembly (first focal plane) remains in the same visual proportion to the target across the riflescope’s entire range of magnification. The hunter will perceive this as a change in reticule thickness with changes in magnification. In reality the reticules are actually in proportion to the target. It is a system often found on European riflescopes and is not particularly liked in Africa and America, but provides good range-finding capability.

Reticules placed behind the erector assembly (second focal plane) will always stay the same size.

Fixed Power Riflescopes

Fixed power riflescopes are becoming increasingly scarcer as they do not offer the convenience of varying the magnification to suit the size of and distance to the target. Such riflescopes offer a singular magnification, but actually work very well.

Focusing Riflescopes

Not everybody has 20-20 vision and riflescopes must be adjustable to suit different eyes. Riflescope focus adjustment is effected by adjusting the ocular (rear) lens group.

Hunters without refraction errors can use a simple procedure to focus their riflescopes. Relax the eyes by looking at something distant without objects the eye can fix on, such as the cloudless sky. Turn the focus ring on the rear end of the riflescope fully to one side. Then bring the riflescope in position in front of the aiming eye and hold it at the same distance that it will be when shooting. Look THROUGH the riflescope and not at the reticules. If the reticules appear fussy or have a ghost image, adjust the ocular bell until they appear focused when executing the test. Do not keep the riflescope in front of the eye for more than a few seconds otherwise the eye will adapt. Then execute a half-turn on the adjustment ring and repeat the process until at some stage the reticules immediately appear sharp when the riflescope is peeked through.

Lens Coating

It is obvious that the more of the light that falls on the objective (front) lens that makes it out the ocular (rear) lens the better the hunter will see. A riflescope that only allows 60 % of the light that reflects on the objective lens to pass into the eye is not as good as one that allows 97% of such light to pass into the eye.

It is a well-known fact that glass does not allow all light that falls on its surface to come through. Approximately 4% of the light that falls on untreated glass is reflected at each surface where glass and air meet. This figure is equally valid for the surface where light enters glass than for the surface where it exits from glass. Because riflescopes easily contain ten lenses, 40% or more light can theoretically be lost in the process of passing through it.

The problem of light reflection and loss was largely solved by Professor Olexander Smakula (1900 – 1983) of the German firm Zeiss during the 1930s by coating lens surfaces with a thin layer of refractive fluoride and other chemicals. This process was extremely successful. These days, riflescope lenses are coated with numerous layers of chemicals, and some manufacturers claim light transmission through their riflescopes to be as high as 99%. Bear in mind that different light conditions and different eye conditions and colour-blindness levels cause hunters to experience different coatings differently. Some eyes react well to certain types of coating and others not.

Light Transmission – Relative Brightness of Riflescopes

The prospective riflescope purchaser should avail himself of two other terms – the Relative Brightness and the Twilight Factor of a riflescope. Otherwise he will be misled by the performance claimed for a riflescope in poor light conditions.

For many years most riflescope manufacturers published relative brightness indexes for their riflescopes, thereby propagating that a higher brightness factor meant better twilight performance. Relative brightness as a term bandied about is nothing but the square of the riflescope’s exit pupil diameter. The exit pupil diameter is, of course, the diameter of the light beam which exits from the ocular lens and can be determined by holding the riflescope at arm’s length. The bright spot visible on the ocular lens is the exit pupil. Because the exit pupil is determined by the amount of light which pass through the riflescope, it had incorrectly been accepted as a good method to determine a riflescope’s ability to function effectively in poor light. This is incorrect.

Simply put, the exit pupil of a riflescope can be increased by enlarging the objective lens diameter, as the exit pupil is the objective lens diameter divided by the riflescope’s magnification, i.e. 42mm (1,65″) lens diameter divided by 7x magnification = 6mm (0,236″) exit pupil. The brightness index of a riflescope with a 6mm exit pupil is 6×6 = 36. Another example is a 56mm (2,2″) lens diameter divided by 7x magnification which results in an 8mm (0,315″) and a brightness factor of 8×8 = 64. The latter’s relative brightness is 64 which is better than the 36, because the exit pupil is larger.

The relative brightness of two lenses with the same objective lens diameter will differ if their magnifications differ. For example, divide a 56mm lens by 8 magnification, and you will end up with a 7mm (0,275″) exit pupil. If you divide a 56mm lens diameter by 4X magnification it gives a 14mm (0,551″) exit pupil. The riflescope with the smaller magnification has the largest exit pupil and the square thereof will, naturally, also be the largest. Nobody can blame any hunter being under the impression that riflescopes with low magnification are better suited to low light conditions than high magnification.

The truth is that the pupil of the human eye can only open up to a certain extent: ±0.2” (±5mm) in hunting conditions. At that aperture the eye can, like a camera, only absorb and utilize a certain amount of light, being of 0.2” (5mm) diameter. A large diameter light beam cannot penetrate the pupil. Just like a 4” (100mm) pipe cannot accommodate all the water from an 8” (200mm) pipe in the same time without increasing pressure. Riflescopes cannot increase light’s pressure. So, the relative brightness figure is a useless consideration when evaluating a riflescope intended for twilight use and hunters should not be misled by it.

Light Transmission – Twilight Factor of Riflescopes

A riflescope with a high magnification is better suited to poor light conditions because it shows more detail. This is proved and measured by the so-called twilight factor (TF). The twilight factor is determined by multiplying the objective lens diameter with the riflescope’s magnification and then determining its square root.

Example 1 TF = √ lens diameter x magnification
TF = √ 32 x 4
TF = √ 128
TF = 11,3
Example 2 TF = √ lens diameter x magnification
TF = √ 32 x 8
TF = √ 256
TF = 16

The riflescope in example 2 has a higher twilight factor and is therefore better suited to hunting in poor light. What it all boils down to is that a larger objective lens diameter or a higher magnification are both positive factors in poor light.


Objective Lens Diameter

The size or diameter of a riflescopes objective lens is governed by the wave theory of light. Light rays move from one point to another in a wave pattern, like ripples in a pool. This causes the outline of an image to become somewhat hazy, almost as if the object is vibrating.

Because of this vibration it is, practically speaking, virtually impossible to observe an absolute perfect point image of any object through a lens. Each point of an image consists of a spot of light with a diffraction ring surrounding it. This ring is called the Airy disc. The only solution is to increase lens size, thereby admitting a greater area of the wave front and then to concentrate the same tightly for better visual resolution. This can be illustrated by drawing something on a large scale. By reducing its size, certain detail is lost, yet it shows more detail then would have been the case had it initially been drawn on a small scale. In the case of lenses this can only be achieved by using objective lenses with a larger diameter.

In order to use the image reflected on the riflescope’s objective lens, the light must penetrate the eye. The light that penetrates the eye must be concentrated in a beam with a diameter not exceeding normal pupil diameter, that being 0.275” (7mm) in pitch darkness and about 0.197” (5mm) in light suitable for hunting. If this image beam (exit pupil) is larger than the pupil, the eye will be unable to see the whole image reflected on the objective lens.


Parallax is normally defined as the apparent displacement of an object relative to another because of a shift in the point from which the object is viewed.

This can be practically illustrated with the same example used to determine the dominant eye of a shot – with minor adaptions. Stretch an arm with the hand in the classical hiking gesture out in front of the head, simultaneously aligning the thumb with an object a few metres away whilst keeping one eye closed. Switch eyes without moving the hand or head at all. The thumb will not be lined up with the object anymore. Yet neither the thumb nor the object has moved. It is just the point or angle of observation that has changed. If the thumb is held against the object the apparent movement, because of different observation points, will be minimal or non- existent.

Parallax is one of those terms that baffle most hunters simply because it sounds complicated. In reality, the aspects regarding parallax that the hunter has to master are few and relatively simple, as it is unnecessary to understand or use any mathematical means.

The existence of parallax in all riflescopes is easily determined. Place a riflescope on a solid rest and aim it at an object about ten metres off. Then move the aiming eye horizontally to and fro behind the scope. The reticules will appear to move relative to the point of aim. Yet it is not the case. Once again it is merely the point of observation that moves.

From this we can deduct that if the aiming eye pupil is not exactly aligned with the centre of the exit pupil of the light rays, an angle is created between the eye’s line of sight and the axis of the light moving through the riflescope. This causes parallax and results in a point of impact differing from the point of aim indicated by the reticules to the off-center aiming eye.

This error is so slight that it can be ignored during short-distance hunting. The effect is more pronounced across longer ranges. A long-range hunter normally has sufficient time to align his eye properly, thereby eliminating parallax. For this reason it is important to choose a riflescope with a small exit pupil for long-distance use. Even though the manufacturer claims it to be parallax-free, it is not parallax-free over all distances. That is why a parallax adjustment feature has been introduced on riflescopes to be used at long range. If hunting distances are short or hunting conditions of such a nature that aiming time will be short, riflescopes with larger exit pupils will offer an advantage.

Although the time parallax and its effect are now understood, it remains necessary to explain the reason for its existence.

At the discussion of erector lenses it was stated that the reticules must be placed at the focal length of these lenses to present a clear image of target and reticules, and to place both on the same visual plane.
We all know that a magnifying glass must be held a specific distance from an object in order to present the clearest image to the eye. In layman’s terms it can be said that the moment the magnifying glass is moved away from that point, the focal length does not coincide with the viewer’s eye and the image blurs. A riflescope has the same effect. Because the reticules cannot be moved around in the scope due to design, it follows that the lenses must be calibrated to form their focal points at the reticule position. This, on the other hand, means that the relevant lens group can only be a specific distance away from the target.

Riflescope manufacturers, therefore, choose an arbitrary distance for the target according to where the lenses are calibrated to have the correct focal length. In riflescopes intended for centerfire hunting rifles this distance normally is 100 metres or 100 yards.

The hunter virtually never finds a target at exactly the distance his riflescope is calibrated for and so the focal point inside the riflescope does not form exactly at the desired point where the reticules are situated. This results in the reticules and the image not being on the same plane. The same phenomenon as with the thumb example occurs when the point of observation is moved. Parallax occurs. The nearer the distance between the target and the relevant lens is to the arbitrary 100 metres, the nearer to the desired point the focal point forms and the smaller parallax becomes. The further beyond 100 metres the target stands the progressively more pronounced parallax again becomes.

Some riflescopes, especially high magnification target and silhouette riflescopes being used over known distances, are fitted with an external adjustment ring on the objective bell or a parallax adjustment knob on the turret. This enables the shot to focus the riflescope for each distance over which the riflescope is used in order to eliminate parallax.

Rangefinding Reticules

These riflescopes were originally developed for the military and originally employed a so-called mil-dot system in terms of which the sniper bracketed his target between the cross on the scope reticule and a series of dots, and then calculated the range to the target. It is quite accurate.

Civilians generally do not take the trouble to master the mil-dot system and a variety of simpler systems have been developed for them. This ranges from bracketing animal bodies between sets of lines to a variety of other systems. The advent of portable laser rangefinders has largely eliminated the need for this kind of system, but it remains popular for some reason.

Resolving Power – Human Eye

The resolving power of the average human eye is about one minute, or a 16th°, which means that a normal and healthy human eye can distinguish an object (say blocks on a chessboard) of about 1” (25,4mm) in diameter at 100 yards. If the chess board is moved further afield, the human eye will find it progressively more difficult to distinguish each square until a point is reached where the chessboard will appear grey.


Resolving Power (Magnification) – Riflescopes
The resolving power of a riflescope is the relationship between the riflescope’s magnification and the human eye’s resolving power. A riflescope with a 4x magnification will enable the human eye looking through it to distinguish a square (or any object for that matter) over four times the distance the naked eye is able to. Put differently: Over any given distance such a riflescope will enable the shot to distinguish a square a quarter of the size that the naked eye can. The ability of any riflescope to distinguish an object and its details depends on:

  • The type of glass used;
  • The quality of such glass;
  • The degree to which aberrations have been corrected;
  • The diameter of the objective lens.

As a result of modern technology there is a large number of types of optical glass in existence, each with its own properties. Quality and uniformity of the end product depends on the ability of the manufacturer to maintain batch-to-batch consistency.

Trajectory Compensating Riflescopes

See Ballistic Turrets above. Such riflescopes are specifically designed to change the point of impact according to the distances over which the shooting is done. These riflescopes contain certain distance settings. In other words, it is adjustable for distances like 100m, 200m, 300m and so forth. Such a riflescope is sighted in at say 100m and can then be calibrated to be on target at any of the other distance settings when adjusted.

Variable (Power) Riflescopes

A variable power riflescope offers the hunter a range of enlargements (magnification options). If he hunts at close range or large animals, the hunter can reduce the magnification and, if the animal is small or distant, he can increase the magnification to see the target much more enlarged.