# Position of the principal points of a telephoto lens system

• MissScience33
In summary, the conversation discusses the determination of the principal points of a telephoto lens, which involves measuring the focal lengths and using f=PF. There is confusion about the positions of the principal points and whether the direction should be towards or away from the lens. It is suggested to use a laser beam to locate the planes, with the rear plane being defined where the ray appears to cross the rear principal plane at the same distance from the axis.
MissScience33
Hi everyone,
for a lab I need to determine the position of the cardinal points of a telephoto lens. The focal points were determined experimentally, and the focal length given on the lens is 200mm. The principal points should be determined with f=PF.

In all the textbooks, the principal points mostly find themselves back within the thick lens/lens system, or very close to it if it is for instance a meniscus lens. For a telephoto, both principal points should find themselves back in the object space.

But if I draw the principal points such that the focal lengths go from the focal points towards the lens, the rear principal point finds itself closer to the front focal point, and the front principal point is closer to the rear focal point. I think this is strange since the focal length should then be the shorter distance between the (in my sketch) rear, respectively front focal point and the front, respectively rear principal point.

I was wondering if due to the fact that in a telephoto, there are two lenses(in theory, in practice there are apparently more to prevent aberrations I think), with a negative and a positive focal length, in order to find the principal points, one should go in the same direction, towards the object space for both? Or maybe in opposite directions, but not towards the lens? This seems slightly weird to me if I understand the theory correctly, but maybe I missed something with the signs of the radii of curvature, or the focal lengths?

Or is there maybe a problem with the positions of the focal points?

Thanks for any input!

Last edited:
MissScience33 said:
Hi everyone,
for a lab I need to determine the position of the cardinal points of a telephoto lens. The focal points were determined experimentally, and the focal length given on the lens is 200mm. The principal points should be determined with f=PF.

In all the textbooks, the principal points mostly find themselves back within the thick lens/lens system, or very close to it if it is for instance a meniscus lens. For a telephoto, both principal points should find themselves back in the object space.

But if I draw the principal points such that the focal lengths go from the focal points towards the lens, the rear principal point finds itself closer to the front focal point, and the front principal point is closer to the rear focal point. I think this is strange since the focal length should then be the shorter distance between the (in my sketch) rear, respectively front focal point and the front, respectively rear principal point.

I was wondering if due to the fact that in a telephoto, there are two lenses(in theory, in practice there are apparently more to prevent aberrations I think), with a negative and a positive focal length, in order to find the principal points, one should go in the same direction, towards the object space for both? Or maybe in opposite directions, but not towards the lens? This seems slightly weird to me if I understand the theory correctly, but maybe I missed something with the signs of the radii of curvature, or the focal lengths?

Or is there maybe a problem with the positions of the focal points?

Thanks for any input!
I don't understand what you are trying to do- is this a ray tracing exercise, or are you trying to locate planes for an actual lens sitting on a bench?

Andy Resnick said:
I don't understand what you are trying to do- is this a ray tracing exercise, or are you trying to locate planes for an actual lens sitting on a bench?
I'm trying to locate the planes for a real telephoto lens.

MissScience33 said:
I'm trying to locate the planes for a real telephoto lens.
Hmmm... I think it's a little tricky.

Try aiming a raw laser beam parallel to the optical axis, laterally displaced by a given distance and then measure the angle the beam when it emerges from the lens. I think you can then use trig to locate the rear plane, defined where the ray emerging from the lens appears to have crossed the rear principal plane at the same distance from the axis that the ray entered the lens. Reverse the setup to locate the front principle plane.

## 1. What are the principal points of a telephoto lens system?

The principal points of a telephoto lens system are the two points on the optical axis where light rays converge or diverge without undergoing any angular deviation. They are typically denoted as P and P', with P being the front principal point and P' being the back principal point.

## 2. How are the principal points of a telephoto lens system determined?

The position of the principal points is determined by the design of the lens system, specifically the curvature and thickness of the lens elements. They can also be calculated using the lens maker's formula, which takes into account the refractive indices and radii of curvature of the lens elements.

## 3. What is the significance of the principal points in a telephoto lens system?

The principal points play a crucial role in determining the magnification and image formation of a telephoto lens system. They also help in determining the minimum focusing distance and the depth of field of the lens.

## 4. Can the position of the principal points be changed?

Yes, the position of the principal points can be changed by altering the design of the lens system. For example, changing the curvature or thickness of the lens elements can shift the position of the principal points.

## 5. How do the principal points affect the overall performance of a telephoto lens system?

The position of the principal points can affect the overall performance of a telephoto lens system in terms of image quality, distortion, and aberrations. A well-designed lens system with properly positioned principal points can result in sharper images with minimal distortion and aberrations.

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