Reticles - First Focal Plane vs Second Focal Plane

"Why on earth would I want the reticle to get thicker when I zoom in?"

I had that thought more than thirty years ago when I read about the funny riflescopes that a little company called Schmidt & Bender was making in Germany. Apparently their scopes were really good. Apparently, having a zooming obelisk for a reticle was normal there. What I was clear about was that their scopes were eye blinkingly expensive. It all sounded like a disease, but it did make me curious. "There's got to be something in this," thought the penniless student. However, I had no option but to archive the thought.

When the archive was opened in mid 2012 I found that the rest of the world was paying more attention to European scope designers. More scopes were being offered with reticles in the first focal plane. Reticles that grow! Here's how that works.

Light from the sun or another source falls onto a scene in front of us and hits objects which absorb some of it. The rest reflects off in all directions. Objects that have absorbed hardly any of the light appear white to our eyes. Their colour is a mix of nearly all the light in the visible spectrum. Objects that are black have absorbed most of the light in the visible spectrum.

Imagine an object that is tiny; as small as the eye can see. A spec of pollen sitting on the surface of a large oil painting. It's a landscape painting. Light scatters off the pollen in all directions. Imagine standing one hundred meters away from the painting, spying at it through an aluminium tube. Draw lines in the air from the spec of pollen to the hole at the front of the tube. Draw enough of those lines and the shape of a long, narrow, solid cone will be formed. Think of this as a cone of light rays that have reflected from the pollen and have reached the tube.

Now put a group of lenses inside the front of the tube. These lenses allow the cone of light rays to pass through into the tube but bend each ray inwards so that the cone rapidly but smoothly collapses back down to a point. Let's say that the lenses we've chosen cause the cone of light rays to collapse to a point after travelling about 15cm into the tube.

Here's the tricky part. Look back out at the big painting, a hundred meters away. Visualise how the entire painting around the spec of pollen is made up of a billion other tiny light reflectors. A cone of light comes from each of these points, reaches the lenses at the front of the tube, goes through them and collapses down to its own point. All of these points end up arranged in perfect order to form an image of the oil painting. The place inside the tube where this image is formed is called the first focal plane.

Take a thin disk of clear glass and scratch some lines on it. Make a cross in the middle. Put this disk of glass in the tube where the image is formed and we have a reticle positioned in the first focal plane.

This diagram shows the first and second focal planes. For this scope, the reticle is in the second focal plane.

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Why is it called a focal plane?

The painting is a plane, perpendicular to our direction of view. The image of the painting formed inside the tube is a plane of focussed points of light. We've chosen our lenses well and all of the cones of light coming from the painting have been brought down to points, nicely focussed, at the first focal plane.

The painting has been standing in a three dimensional woodland scene, out in the real world. When the painting is taken away, only the parts of the scene that lie in the real world plane that it occupied will be shown in perfect focus in the image at the first focal plane. Perhaps the grass it was standing on or the tree it was leaning against. Objects in front of or behind the real world plane will be out of focus at the first focal plane, to some degree, depending on how far from the real world plane they are. They're out of focus because the cones of light coming from them collapse down to their points before or after reaching the first focal plane. When these cones of light reach the first focal plane their cross section is a disk of light, rather than a point of light. This makes them blurry at the first focal plane. The further an object is from the real world plane, the larger the disks of light coming from it will be at the first focal plane and the blurrier the object will appear to be in the image at the first focal plane.

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The cones of light rays coming from the scene go through the lenses as directly as they can, bending only as much as the lenses make them. The light from an object at the bottom left of the scene ends up at the top right of the image formed at the first focal plane. Light from the top centre of the scene ends up at bottom centre of the image. The image at the first focal plane is upside down and left to right. Good luck trying to hunt with that!

After a cone of light rays goes through the front lens and comes to a point inside the tube, the rays keep going. The light rays that make up the cone that has collapsed to its point cross over and continue on, creating a new cone that starts opening out. This happens with all the cones of light that have come from the scene and have gone into the tube.

We want our image of the woodland scene, now with our first focal plane reticle included, to be the right way up and the right way around. To achieve this, put a new group of lenses in the tube, a little further along from the first focal plane. These lenses stop the cones of light from expanding and send them along the tube shaped more like cylindrical beams. They also direct the beams towards and across the centreline of the tube. Put another group of lenses further along, shaped so that the cylindrical beams that pass through them are changed back into collapsing cones, which tighten down to points even further along the tube. The place where all of these cones of light become points of light, arranged into an image of the scene, is called the second focal plane.

Because the beams and cones of light have been moved across the centreline of the tube, the image at the second focal plane is now the right way up and the right way around. To look right the image has been erected, so let's call the lenses that did this the erecting optics.

Not only do we want the image the right way up, we want variable magnification. OK then, we'll need a shorter, narrower tube that fits neatly inside the main tube. Put the erecting optics at the front and rear ends of this internal tube and slide it back and forth. This makes the image at the second focal plane zoom in and out. And here comes the clincher. Because the reticle at the first focal plane has already been mixed in with the rays of light before they reach the erecting optics (which are now also the zooming optics) the reticle zooms in and out as well. When the zoom ring is turned, the first focal plane reticle grows and shrinks together with the image of the real world that is formed at the second focal plane.

Right. Nice to know. But why is that useful?

It's going to get a bit technical so I have to use italics.

If a variable power riflescope has its reticle located in the first focal plane, when the zoom ring is turned the reticle grows or shrinks together with the scene being viewed. Markings on the reticle will stay in proportion with the scene when they zoom together. The markings on the reticle can be accurately etched so that an interval between them corresponds with a particular angle of view in the real world, say, one thousandth of a radian. Because the markings and the scene stay together as they are zoomed, the angle of view defined by the markings will remain constant, regardless of the zoom setting.

The scope can be designed so that the angle of view defined by particular markings is matched to a certain number of clicks with the turrets. For example, the design could be that it takes 10 clicks to move the scene one thousandth of a radian past the reticle. This is a common design in Europe. It's also common to call one thousandth of a radian a 'milliradian', or even a 'mil'.

So now, when using the scope on a rifle, if the first bullet lands one milliradian to the left of the target, the turret can be turned 10 clicks to move the image to the right and the next shot will hit (provided an accurate rifle like a Mauser M03 is being used ;-) ). This will work with any zoom setting and at any range.

Let's read that last sentence again. 'This will work with any zoom setting and at any range.' Now that's useful.

Second Focal Plane.

If the reticle is placed at the second focal plane, its size and shape remains fixed when the image is zoomed. This is because the light beams have already passed through the erecting optics tube and are already zoomed in or out before the reticle interferes with them and becomes part of the image.

What are the advantages of having the reticle in the second focal plane? Well, for general hunting, when quick shots are often needed, it's good to know that the reticle will look exactly like it did last time, regardless of what has been done with the zoom setting since. It also ensures that the designer's choice of 'momma bear' thickness for the crosshair - thickness that is 'just right' - will apply at all zoom settings. The crosshair won't appear to be too thin at low magnification or too thick at high magnification.

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For completeness in constructing our riflescope, let's put some lenses at the rear of the tube. These will take the beams of light that have passed through the second focal plane and organise them nicely for our eyes. If we mount these in a tube that threads into the main tube we'll be able to screw them in and out so that we can adjust for our eyes and make sure the reticle is sharply focussed. If we are prepared to allow the reticle to be a little out of focus we can use this rear group to finely adjust the location of the focal plane to one side of the reticle or the other and hence adjust the location of the plane that will be in focus out in the real world. More on this in relation to the Zeiss Victory HT scopes later.

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As a example of how first focal plane reticles can be useful, imagine a father and son out shooting rabbits at 500 meters with Mauser M03s, in 243 Winchester and 6.5x55. Both rifles have first focal plane scopes with milliradian divisions on the reticles and turrets with 10 clicks to the milliradian. The son has adjusted his scope for the range and shoots with the 243 while the father watches through his scope on the 6.5. He sees the bullet impact the grass a little low and a little to the left. The rabbit crouches but doesn't run. The father measures the miss distance with his reticle and says, "2 clicks up and 2 clicks right." The son adjusts with a 'click-click' and a 'click-click' and the next shot hits. :-D

This video snippet shows Thomas Haugland quickly adjusting a scope that has the reticle in the first focal plane, to get shots on target.