All About Scopes - V

In our last few posts, we studied telescopic sights from the outside and in our previous post, we studied one part that is inside the scope, namely, the reticle. We also talked about terms like First Focal Plane (FFP) and Second Focal Plane (SFP) in our previous post. In today's post, we will look into the parts of a telescopic sight in more detail and find out what FFP and SFP really mean.

Before we dive into a telescopic sight, let us first study lenses, in particular, a type of lens called the biconvex lens (also sometimes called a converging lens). A biconvex lens is thicker in the middle and thinner at the edges. It is typically made of a transparent material, such as glass. Since glass has a greater density than air, light bends as it passes through it (you can observe the same effect if you look into a pool of water, as objects at the bottom of the pool appear to be at a different location than where they really are, due to the light rays bending as they enter it.) In a lens of this type, when light from a great distance passes through it, the light is concentrated to a spot on the other side of the lens, called the focal point, as shown in the diagram below:

Image licensed under the GNU Free Documentation License Version 1.2

The distance between the center of the lens and the focal point is called the focal length of the lens (marked as 'f' in the figure above). Before you start yawning after reading this material, you may actually be familiar with the concept of focal length, but not realize it. As children, many of us have used a magnifying glass to burn holes into a sheet of paper (admit it, you did it too). The trick is to move the lens up and down to adjust the focus, until a tiny concentrated image of the sun appears on the sheet of paper. When the paper starts to burn, the distance between the lens and the sheet of paper is the focal length of the lens.

Now let us consider an object as viewed through a lens, as shown in the image below:

Image licensed under the GNU Free Documentation License Version 1.2

When the object is at a distance S1, at a great distance from the lens, an image can be projected onto a screen at a distance S2 on the other side of the lens (where S2 is much smaller than S1). We will not study the cases where the object is located at a closer distance to the lens (e,g. if it is closer than the focal length or twice the focal length), as these are irrelevant to our object of study.

The main thing to notice in the above diagram is that the image is upside down because of the way that the lens bends the light reflecting from the object. As you can imagine, this is not very useful for telescopic sights because people aren't used to seeing things upside-down. We will study how this is rectified later.

Now that we've studied how light passes through a single lens, let us study how light passes through two lenses (i.e.) a simple refracting telescope similar to one used by Galileo in the 17th century,

Click on the image to enlarge

The above image shows how light passes through two lenses. The lens on the left is the larger objective lens, which has a longer focal length, and the lens on the right is the eyepiece lens (otherwise called the ocular lens). We encountered these terms a few posts ago, when we studied the external parts of a scope.

As you can see from the images above, the two lenses collect more light than a human eye can by itself, and give the user a brighter magnified image. Note that because of the way that the light bends, the image that the user sees is upside-down. The fact that the image appears upside-down doesn't matter when viewing symmetrical objects such as stars, the planets, the moon etc. However, it does definitely matter when viewing targets on the earth, as users prefer to see their targets aligned in the proper direction.

Therefore, scopes work around this issue by having another set of lenses in between the objective lens and the ocular lens. These intermediate lenses also flip the image, therefore when it comes out of the ocular lens, the double inversion causes the image to be turned back to the correct direction, the way that most users like to see it. The image below shows how this works:

Internals of a telescopic sight. Click on the image to enlarge.

Light passes through the objective lens and the image is inverted, as we have already seen a few paragraphs above. It then passes through another set of lenses, labelled as the picture reversal assembly (also called "erector lenses") in the image above. These lenses serve to invert the image again, which means by the time it passes through the ocular lens, the image is flipped back to the correct direction. In variable power scopes, there is a mechanism to allow the erector lenses to be moved back and forth, which changes the magnification power of the scope.

Also note that the first focal plane (FFP) reticle is located at the focal length of the objective lens. There is also a second focal plane (SFP), which is located at the focal length of the erector lenses that comprise the picture reversal assembly. The reticle can be placed at either the FFP point or the SFP point. We studied the implications of placing the reticle at FFP vs. SFP a couple of posts ago and also in our last post.

We will study more about the internal parts of a scope in the next post.

All About Scopes - IV

In our last post, we studied some details about the reticle inside a scope. In today's post, we will look into some more uses of reticles, namely rangefinding. We had actually dealt with this topic some time ago, when we talked about telescopic sights.

The key to rangefinding in most scopes is to compare an object of known height or width against a series of markings on the reticle, to determine how far away it is. We will see how this works with a few examples.

Reticle from a Russian PSO-1 Scope, as used by the SVD rifle. Click on the image to enlarge. Public domain image.

The above image shows the reticle from a PSO-1 scope, which was originally designed for use by the Soviet military Dragunov SVD sniper rifle. When this was originally introduced in 1964, it was the most advanced mass-produced scope available. This scope is a fixed power scope with 4x magnification. It has several markings on it. The top chevron (^) mark is used as the main aiming mark. The horizontal marks (10...10) are used for adjusting for windage and also allow to lead the target, in case it happens to be moving. The horizontal marks can also be used for rangefinding, if the width of the target is known beforehand. Each marking on the horizontal 10..10 marking is spaced at one milliradian interval, therefore the calculation for finding distance can be determined by the following formula:

D = S / mils * 1000

where
D = distance to target in meters
S = Known height or width of target in meters
mils = Number of markings wide that it appears when viewed through the scope

Say the user is viewing a Land Rover vehicle, which is known to measure about 4 meters long (i.e. 13.12 feet long). Let's say that when it is viewed through the scope, it measures up to 8 markings long. Then, we put S = 4, mils = 8 in the above formula and calculate D = 4/8 * 1000, which works out to 500 meters. Therefore, the Land Rover is approximately 500 meters away from the scope.

Also notice the curved line on the lower left quadrant with the numbers (10..2). This can also be used to measure distance to the target, in this case using a human for range finding. The markings assume that an average human is 1.7 meters (5 feet 8 inches) tall. The user simply aligns the scope so that the person's feet touch the bottom horizontal line and see which marking the person's head touches, as shown in the image below:

Public domain image

In this case, the person's head touches the 4 mark, which means that the person is about 400 meters away. Using this set of markings, the user can determine ranges from 200 to 1000 meters.

The PSO-1 scope has a bullet drop compensator (BDC) to adjust range in 50 meter increments from 100 meter to 1000 meter ranges. Therefore, once the range to the target is determined, the user can turn the knob and adjust the elevation to correspond to the appropriate range and then align the target with the top chevron mark (^).

Notice that the scope also has other chevron marks (^) below the first one. These are used to shoot at ranges beyond 1000 meters. The user sets the elevation to the maximum of 1000 meters, then uses the other chevrons to line up to 1100, 1200 and 1300 meters respectively.

Now we'll look at another reticle.

Reticle used by Schmidt and Bender scope. Public domain image.

The above reticle is used by scopes made by Schmidt & Bender. Note that the center of the scope has several dots in the horizontal and vertical lines. These are called mil-dots and each dot corresponds to 1 milliradian. Therefore, if the width or height of an object is known, the user can determine the range by counting the number of dots that it covers and then using the same distance formula that we saw above for the PSO scope. Therefore, if an average person, who is about 1.7 meters tall (or 5 feet 8 inches tall), covers 4 dots when viewed in the scope, we can take S = 1.7, mils = 4 and plug it into the formula D = 1.7/4 * 1000, which works out to 425 meters.

There is also another way to quickly compute the range with this reticle, without doing any arithmetic. Note that the bottom of the reticle, there is a long horizontal line and above it are a series of smaller horizontal lines in a step pattern. These lines can be used to quickly estimate the distance to a target, using a human as the scale. To estimate distances between 100 and 250 meters, the user simply frames the target's head between the lines as shown below:

Public domain image.

The average human head is around 0.25 meters high. The two lines that best frame the top of the helmet to the chin tell the distance to the target.

For longer ranges, the same horizontal lines can be used, except that the user frames the top of the target's head to the belt buckle between the two lines.

Public domain image

Using this, the user can measure distances between 400 and 1000 meters.

Note that in both these instances, the scopes are fixed power models. Therefore the user cannot adjust the magnification power and the rangefinding calculation is easier.

For scopes with variable power magnification, the method of rangefinding depends on whether the reticle is placed on the first focal plane (FFP) or second focal plane (SFP).

Recall in our last post, we mentioned that if the reticle is placed on the first focal plane, the size of the reticle resizes with the magnification, so if the user zooms into the target, the reticle also appears to enlarge in size correspondingly. So, if a target measures 4 mil dots at 3x zoom, it will still measure 4 mil dots at 10x zoom, when using a FFP reticle. Therefore, for a variable power scope using a FFP reticle, the range calculation formula is the same as that of the fixed power scope, D = S/mils * 1000.

We also mentioned in our last post, that in a reticle placed at SFP, the size of the reticle does not change with magnification power. Therefore, for a SFP scope, the mil-dot range estimation is calibrated accurately only at one particular magnification power, generally at the highest magnification power setting, or sometimes at the middle magnification power setting. Some SFP scopes have an index mark on the power ring, to show at which magnification power setting the mil dots are accurate (for instance, some manufacturers set it at 10x power, Bushnell generally sets theirs at 12x power). The formula for range estimation changes a bit in this case. Assume a SFP scope where the mil-dots are calibrated accurately at 10x magnification power. The distance formula for this scope is:

D = (S/mils) * (mag/10) * 1000

where
D = Distance to the target in meters
S = Width or height of the target in meters
mils = Number of markings covered by the target
mag = Magnification power of the scope.

As you can see, with a SFP scope, the range calculation is a bit harder to do because it depends on the magnification power setting on the scope. Therefore, some users usually set their scope at the power setting that it is calibrated at and leave it there, so that they don't have to do the extra math. For instance, in the above example, if the magnification power is set to 10x (i.e. the same magnification power that it was calibrated at), the formula simplifies to D = S/mils * 1000 (i.e.) the same formula as for a fixed power scope. Alternatively, if they change the magnification power, they change it to half or double of the calibration setting. For example, a Bushnell Elite 4200 6-24x40 variable power scope is calibrated at 12x magnification power, so if the user wants to change the magnification power, they usually select 6x or 24x, so that the range calculation can be modified by dividing or multiplying by 2. If the user chooses any other magnification power settings, the math becomes correspondingly harder.

This is why many military scopes use fixed power scopes, to reduce the amount of math calculations that the user has to do, and also avoid the chance that the user makes an incorrect calculation due to not paying attention to the magnification power setting of the scope.

All About Scopes - III

In our last couple of posts, we studied about different types of scopes and what they look like from the outside. In today's post, we will look at some of the stuff inside a scope. Specifically, we are going to study about a part called the reticle.

We actually dealt with reticles a little over four years ago, when we studied telescopic sights originally. A reticle is a device consisting of fine lines, which is embedded into a telescope and helps the user to line up a target precisely.

The classic image of a telescopic sight is a target centered around two crosshairs, such as the image above. This is usually what is shown in movies and TV shows. However, there are many different types of reticles, which we will study.

Different types of reticles. Public domain image.

Thanks to movies, most people are familiar with the Fine Crosshair type of reticle above. Fine crosshairs allow the user to see more of the target and do not block out much light. However, it is easier for the user to lose sight of the lines, especially in complex backgrounds. Thicker lines are more visible, but they block out more of the image and lose some precision. Therefore, modern telescopic sights use a mixture of both (i.e.) thicker lines on the outside and thinner lines closer to the middle. Examples of this would be the Duplex Crosshair, the Mil-Dot and the Modern Rangefinding reticle above. The thick lines allow the user to quickly figure out where the center of the reticle is and the thinner lines allow for precision aiming.

Back in the day, the crosshairs of reticles were made of  natural fibers, such as hair or spiderweb. Later on, they were made of thin wires (and many scopes still use wire crosshairs to this day, especially cheaper ones). The wires are mounted on the inside of the telescope tube. By flattening the wire in different places, the manufacturer can make Duplex Crosshairs or Target Dot type crosshairs. The nice thing about wire reticles is that they don't block out much light and are very durable.

Another technique to make the crosshair lines is to etch the lines onto a thin plate of glass, using a diamond cutter. The thin plate of glass is then mounted inside the scope. The etched lines allow for more complex crosshair shapes, including circles, lines that don't need to touch or have gaps in between. This allows them to have features such as estimating range and bullet drop (such as that seen in the Modern Rangefinding and the SVD type above). The etched lines block off a bit more light and the thin glass plate may reflect some of the light back instead of letting it through. Modern scopes usually coat the glass with special coatings designed to minimize the reflected light.

For aiming in low light conditions, many scopes have illuminated reticles. The illumination is usually provided by a few methods. The first is to use a bit of fiber optic cable to collect ambient light from the outside of the scope and deliver it inside to the reticle. Another technique is to use a battery powered LED to provide enough light to illuminate the reticle. While this method requires the user to carry a battery with the scope, it has the advantage that the user can usually adjust the brightness by turning a knob. The user may also be able to change the color of the backlight illumination, if the LED method is used. The third method, which is used in military scopes, such as the Trijicon ACOG, or the British SUSAT sight, is to use tritium, which is a mildly radioactive form of hydrogen, to provide illumination. The tritium slowly decays and emits light as it does so. The nice thing about this is that tritium glows for a long time and could last 11 years or more before the tritium tube needs to be replaced.

As you may have observed in movies, if the crosshairs are backlit, they are usually red, though some products use green or yellow. There is a good reason for this. Red happens to be the color that least interferes with the user's night vision.

Reticles may be mounted inside the telescope tubes in one of two spots: the first focal plane (FFP) or the second focal plane (SFP). For fixed power scopes, it doesn't make any difference which focal plane the reticle is mounted at, but it makes a difference for variable power scopes. If the reticle is mounted at the first focal plane, then the size of the reticle resizes with the target (i.e.) if the user adjusts the magnification to zoom into the target, the reticle also appears to enlarge in size and if the user adjusts the magnification to zoom out of the target, the reticle also appears in decrease in size correspondingly. If the reticle is mounted on the second focal plane (i.e. closer to the eyepiece), then the size of the reticle remains a constant, irrespective of the magnification power. Americans tend to prefer scopes with reticles mounted SFP and this is used in the majority of the scopes. Some high end European manufacturers make FFP scopes on request.

We will study more about the advantages and disadvantage of FFP and SFP scopes, when we study the topic of scopes and rangefinding tomorrow.

All About Scopes - II

In our last post, we looked at some basics of rifle scopes. We will continue our discussion in this post.

As we saw in our last post, there are mainly two types of scopes: the fixed power scope and the variable power scope. The big difference between these two is that the variable scope has adjustable magnification. 

We will now look at how these scopes are specified. Fixed power scopes are usually specified as two numbers separated by x. For instance: 4x32, 12x40 etc. So what do these two numbers mean? The first number is the magnification factor of the scope. Therefore, in a scope marked as "4x32", this means it magnifies the image 4x times (i.e.) the object appears 4 times larger when viewed through the scope, than if it was viewed using just the eye. So what is the second number mean? The second number is the diameter of the objective lens in millimeters. Therefore, in a scope marked as "4x32", this means the objective lens is 32 mm. in diameter. In many cases, the unit of measurement is specified, so instead of "4x32", it may be more clearly specified as "4x32 mm."

A Bushnell 10x40 Fixed Power Scope. Click on the image to enlarge.

In the above image, we have a fixed power 10x40 scope made by Bushnell. What this means is that it has a 10x magnification and the objective lens is 40 mm. in diameter.

Variable power scopes also have similar designations, except that they have three numbers. The first two numbers are separated by a hyphen (-) and the third number is separated by x. For instance: 4-16x42, 6-24x50 etc. The first two numbers indicate the range of magnification power of the scope. Therefore, in a scope marked as "4-16x42", this means that the magnification factor of this scope can be varied between 4x and 16x. The third number indicates the size of the objective lens in millimeters. Therefore, in a scope marked as "4-16x42", the objective lens is 42 mm. in diameter. As with the fixed scopes, sometimes the specification includes the unit of measurement as well, so instead of "4-16x42", it may be more clearly specified as "4-16x42 mm."

A variable power 4-16x42 variable power scope made by Nikon. Click on the image to enlarge.

In the above image, we have a Nikon model M-223 scope, which is a 4-16x42 mm. scope. This is the model we studied in our last post, when we were studying the different parts of a scope.

So, a 10x magnification is better than a 4x magnification, right? Not quite. It is true that the object appears a lot larger on a higher magnification scope, but you see less of the surrounding area through the scope. For instance, if you're looking at a herd of deer through a powerful scope, you can probably see the fur very clearly, but you will be unable to tell which particular deer you're looking at, because you can only see a part of a deer's body through the scope. Also, it is very easy to lose sight of a particular deer if it moves off a bit, because the powerful scope only shows a small area at a time. Bear in mind that with a 10x scope, the field of view of an object at 100 yards (90 meters) is about 2 feet (0.66 meters) diameter. With a lower powered scope, you may be able to see both the head and the body of the deer and can tell which one it is in the herd. 

Higher magnification also reduces the brightness of the image. For instance, if you have two scopes, a 4x40 and a 10x40. They both have the same size objective lens (40 mm.), but they have different magnification power 4x and 10x. The image seen through the 4x40 will be brighter than that seen through the 10x40. This has to do with the exit pupil, which we studied about in the last post. The 4x40 scope has an exit pupil of size 10 mm., whereas the 10x40 has an exit pupil of 4 mm.

A scope with higher magnification is useful against targets at a long distance, but not as useful against targets close by.

Therefore, for general purpose hunting, a scope with magnification in the range of 3x to 10x works fine for many hunters. Some use variable power scopes that work in this range (such as a 3-7x or a 3.5-10x scope), others are perfectly happy with a 4x or 6x fixed power scope, some even go for lower power, such as 1.5x or 3x, because they don't hunt at longer distances. For long distance shooting, scopes with magnification of 9x to 18x or so are used and anything more than that can only be used for shooting at targets that don't move.

For most soldiers, the US military have generally equipped them with fixed power scopes, because soldiers work in stressful environments and a fixed power scope saves them worrying about which magnification factor the scope is currently set at. Most military scopes have relatively low magnification, so that they are useful at ranges where combat usually occurs. The US Army, Air Force and Marines use the Trijicon TA31RCO ACOG sight, which uses a 4x32 fixed power scope. The scope has advanced features, such as dual illumination technology provided by fiber optics and tritium.

US Marine using his ACOG scope. Click on the image to enlarge. Public domain image.

Most other military forces also do the same thing for their soldiers. For example, Canada's soldiers are equipped with a C79 optical sight which is a 3.4x28 scope, British soldiers have a standard SUSAT L9A1 sight which has a 4x25.5 scope, Steyr AUG rifles (used by Austria and Australia) have a built-in 1.5x scope made by Swarovski (the same people that make luxury glass chandeliers and jewelry).

Canadian C79 Elcan sight. Click on the image to enlarge. Public domain image.

Snipers have also traditionally used fixed power scopes until recently. During World War II, German snipers used 4x fixed power scopes and US snipers used 8x scopes made by Unertl through World War II and the Korean war. By the Vietnam era, 10x fixed power Unertl scopes were in use by the US Marine snipers, although a variable power Redfield 3-9x scope was also tried out. The Unertl model MST-100 which is a 10x42 fixed power scope, remained in US Marines sniper service for quite a while (until about 2007 or so). The US Army snipers used the Leupold Ultra M3A 10x42 mm. scope or the Leupold Mk 4 LR/T M3 10x40 mm. scope until recently as well. In the recent years, US snipers have been experimenting with variable power scopes. For instance, US Marine snipers have been working with the Schmidt & Bender 3-12x50 mm. scope and the US Army snipers have been working with the Leupold Mk 4 3.5-10x40 mm., Leupold Mk 4 M1LR/T 8.5–25×50 mm. and Leupold Mk 4 6.5–20×50 mm. ER/T M5 scopes. Sandia National Labs also recently demonstrated the RAZAR (Rapid Adaptive Zoom for Assault Rifles) technology based on a request from the US military to develop a compact zoom rifle scope.

In our next post, we will look further into some of the technologies inside a scope.

All About Scopes - I

Many months ago, we had studied about rifle scopes briefly, when studying different types of sights. In today's post, we will cover the subject in a bit more detail.

There are two types of telescopes available to shooters:

1. Fixed Power Scope - These are simpler and have a fixed magnification factor.
2. Variable Power Scope - These are more complicated and allow the user to adjust the magnification, according to the distance that the target is from the rifle.

To understand more about these two types, let us first look at the main parts of a scope:

A scope made by Nikon.

1. Eyepiece
2. Ocular Lens
3. Exit Pupil
4. Power Ring
5. Windage Adjustment Control
6. Elevation Adjustment Control
7. Objective Lens
8. Eye Bell
9. Objective Bell
10. Parallax Compensation Control

In the above image, 1 is the eyepiece, which is the end of the scope that the user looks through. The eyepiece encloses a smaller lens, called the ocular lens (2), through which the user views the target. The eye piece generally has a focusing control at the end of the sight to obtain a sharp image of the target and the reticle.

The exit pupil (3) is the size of the column of light that comes through the eyepiece: the larger the exit pupil is, the brighter the image. The exit pupil size is defined as the diameter of the objective lens divided by the magnification power of the scope. So, if the diameter of the objective lens is (say) 40 mm. and the scope has 4x magnification, then the exit pupil is 10 mm. For variable power scopes, the magnification can be changed, for instance, from 4x to 10x. This means that, assuming you have the same 40 mm. diameter objective lens as above, the exit pupil will vary from 10 mm. to 4 mm. (i.e.) if you increase the magnification, it will decrease the exit pupil size and vice versa. A smaller exit pupil means the image will appear dimmer and a larger exit pupil means the image will appear brighter. 

The power ring (4) is a feature that is only found on variable power scopes. By turning the power ring, the user can change the magnification power of the scope. This feature is not found in a fixed power scope.

The windage adjustment control (5) allows the user to adjust the scope in the horizontal direction (left or right). The elevation adjustment control (6) allows the user to adjust the scope in the vertical direction (up or down).

The objective lens (7) is the large lens which is further away from the user. This lens concentrates the light that goes through the scope. Larger lenses let more light in and in general, the larger the lens, the higher the magnification power of the scope. Typically, the diameter of the larger lens is measured in millimeters.

The eye bell (8) encloses the eye piece and the objective bell (9) encloses the objective lens. 

Variable power scopes of higher quality have a parallax compensation control (10). Basically, parallax is an optical effect caused by the objective lens not being coincident with the reticle. Therefore, putting the eye at different points behind the ocular lens makes the reticle crosshairs appear on different points on the target, which could cause aiming errors. The parallax compensation control allows the user to adjust for the parallax effect.

Some scopes (both fixed and variable types) also have a brightness control for the scope's reticle, so that the crosshairs can be seen in low light conditions. Some high-end scopes also have a feature called Ballistic Drop Compensation (BDC) which allows the user to adjust for the effect of gravity acting on a bullet (i.e. the amount the bullet drops as it travels a certain distance horizontally).

In addition to all these, we must also define a term which we used above: magnification. This is the ratio of the size of the image as viewed through the scope, compared to if it was viewed by the naked eye. For instance, if the magnification factor is 4x, this means an object appears 4 times larger in the scope than if the object was seen without it.

In the next post, we will study some more details about scopes.