# How a Barlow Works

#### The effect of internal spacing on power amplification

Someone asked how a Barlow lens works.

The easiest way to understand how a Barlow works, I have found, is to consider just the on-axis rays—that is, those rays travelling parallel to the tube. Off-axis rays just confuse the matter at first blush. I will use a refractor to discuss it, but the same principle applies to a reflector or compound scope.

You have, perhaps, seen those cutaway diagrams of a refractor showing a shaft of light shining onto the objective lens. After passing through the objective, that shaft becomes a cone, which narrows to a point—the focal point of the objective. The cone then widens on the other side, where it is captured by the eyepiece and becomes a shaft again—the exit pupil of the scope/eyepiece. This is an approximation, of course, but a useful one. (This just to forestall any protests from the optical designer segment.) It is maybe important to note that the exit pupil is not in general the same as the width of the eyepiece; it is usually quite a bit smaller.

Let's play with some sample numbers. Suppose our scope has an aperture of 100 mm (about 4 inches). If the scope has a focal ratio of f/10, then the focal length is 1000 mm, and the light cone has a length 10 times longer than its width. If the eyepiece has a focal length of 10 mm, the magnification is 1000 mm / 10 mm, or 100x. The exit pupil is then just 100 mm / 100x, or 1 mm. In order to reach focus, the eyepiece must be placed 10 mm in back of the focal point. The distance between eyepiece and objective must therefore be 1000 mm + 10 mm, or 1010 mm.

However, suppose we put a Barlow between the objective and the eyepiece. When we reach focus, the Barlow is actually between the objective and its focal point—it is just a little less than 1000 mm from the objective. It captures the light cone just before it converges to a point. Since a Barlow consists essentially of a negative lens, its effect is to make that cone converge even slower—instead of a ratio of 10-to-1, it might make it a 20-to-1 cone, or a 25-to-1 cone, or a 30-to-1 cone. The exact change depends on how close the Barlow is to the original focal point.

Because the Barlow has stretched the light cone, the focal point is no longer 1000 mm away from the objective. It will be some greater distance away—exactly how far depends on the characteristics of the Barlow. If you've heard of Shorty Barlows, you know that design has a part to play in this. However far it is back, though, the eyepiece MUST STILL BE 10 mm away from the new focal point. And because the light cone is more stretched out, the eyepiece "thinks" it is seeing an f/20 or f/25 or f/30 scope, instead of an f/10 one. Thus, the power amplification is 2x or 2.5x or 3x.

But what makes it 2x or 2.5x or 3x? Is it just the strength of the lens? And how do variable power Barlows work?

Remember that the exact stretching of the light cone depends on how close the Barlow is to the original focal point. The closer it is, the less "time" the Barlow has to change the light cone, and the less stretched out the cone is. In fact, if you put it right at the focal point, the light cone is unchanged and comes out the way it did before you put the Barlow in.

The further in front it is, in contrast, the more stretched out the light cone is. In fact, if you move it far enough in front of the original focal point, the rays coming out of the Barlow will actually diverge and never come to a focus at all.

If you put the Barlow very close to the original focal point, then the new focal point isn't changed very much and is still very close to the Barlow. Since the eyepiece has to be 10 mm behind the focal point in any case, the distance between the Barlow and the eyepiece is relatively short and the power amplification low.

If, on the other hand, you put the Barlow further in front of the focal point, then the new focal point is quite a bit further back from where it would have been, and it now can be quite a distance away from the Barlow lens. In consequence, the eyepiece has to be far away from the Barlow also. The light cone is considerably stretched out, and the power amplification is high.

You can think of power amplification as depending essentially on the spacing between the Barlow and the eyepiece. It makes sense to do so because the usual way to use a Barlow is to put the eyepiece into the Barlow, and then put the whole combination into the telescope and try to focus it as if the combination were just one big eyepiece. If the distance between the Barlow and the eyepiece is 100 mm, then the new focal point has to be 100 mm - 10 mm or 90 mm in back of the Barlow, and you have to rack focus in and out until the Barlow lens is placed in the right position to reach that focus.

That's why a 2x Barlow can work as a 3x Barlow by putting it between the objective and the diagonal. In essence all you are doing is putting more space between the Barlow and the eyepiece.

Variable power Barlows work by allowing the user to adjust the distance between the Barlow lens and the eyepiece. Far-out spacings allow the Barlow to stretch out the light cone a lot and increase power. Close-in spacings require the Barlow the stretch the cone only a little bit and reduce power. The problem is that most Barlows are optimized for a relatively narrow power range. Thus it may work sufficiently well at 2x but be poor at 3x.

Many zoom eyepieces, in turn, are essentially variable power Barlows mated to an eyepiece all in one casing. When you turn the knurled ring, you are sliding the Barlow up and down the eyepiece shaft. The difference between this and the variable power Barlow is that since you will only be using one "eyepiece" with the Barlow, the designer can perform some optimization to make sure that the zoom works at least tolerably well at all powers. Of course, it is always possible that no such optimization will be done, and that is part of why zooms have such a poor reputation among many veteran observers (though that is beginning to change).