Measuring the focal length of a meniscus lens

[Wolstan Dixie]

I have a simple fixed focus and aperture box camera, with no data on it. I can measure the aperture and the shutter speed, I need the focal length. It has a single meniscus lens. I have measured the distance from the centre of the lens to the film plane and it is 46mm. I have then attempted to measure the focal length by using an optical bench and 1/F=1/U+1/V. Despite a deal of care and taking 16 measurements, I get a result of 52mm.

Now, as I understand it, the focal length must be equal to or LESS that the distance from the lens to the film (if you are focussed on infinity you focus nearer by moving the lens forward).

So what is happening - is 1/F=1/U+1/V not valid for meniscus lenses?

 

[AgX]

At a meniscus lens the cardial planes ar not located around the center of the glass, they may be even outside the lens. You should consider this in contrast to a symmetrical bi-convex lens.
At a convex meniscus the cardial planes may be in front of the meniscus, the convex side.

 

[Jim Jones]

The image formed by meniscus lenses was analyzed years before the invention of photography in aids for drawing and painting. In the traditional early box cameras, the simple meniscus lens, concave surface towards the subject, is mounted behind the aperture and the focal distance is measured from slightly behind the lens to the film. This gives the best optical performance for such a lens. In many later box cameras, the lens is mounted in front of the aperture with the concave surface towards the film. This shortens the cameras, but focuses on a slightly curved film plane. The focal distance is measured from just in front of this lens to the film.

 

[Ian C]

A brief explanation of the location of the principal planes (nodal points) of various lens types.

 

[Wolstan Dixie]

Well, this is most illuminating - thanks. It is of course convex outwards. So that explains it. Being a simple box camera I estimate the lens to be 0.5mm thick at the centre, so I think that qualifies as 'thin'. So the point to measure from is (an undefined) distance in front of the lens? 6mm seems rather a lot. It doesn't really help, what I am trying to do is calculate the hyperfocal distance - I suspect the camera is constructed focussed on this, in which case the 46mm would be the image distance of the hyperfocal distance, not of infinity, so I have no way of determining the focal distance. The F in the formulae is presumably this virtual F from a point in front of the lens, not the actual infinity focus to the lens?

 

[AgX]

Principal.... no idea what made me write above cardial...

 

[Nodda Duma]

This is what you need:

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/priplan.html


Knowing the radius of curvatures would be useful as well as thickness and index.
Index assume 1.52

Thickness is center thickness, probably 3mm

Radius calculate from shape factor.

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/aber.html

Or measure with a spherometer.

 

[AgX]

What about about applying the Bessel procedure for establishing the focal length in this case?

 

[Nodda Duma]

It could be used, although I found in the past it was sensitive to measurement error.

For reference:

https://www.3bscientific.com/PhysicsExperiments/UE4010100_EN.pdf

 

[ic-racer]

I was trying to work it out using the simple lens formula, solving focal length for different magnifications but got caught out by the math. I think that Bessel may have solved it that way.

 

[alanrockwood]

...In many later box cameras, the lens is mounted in front of the aperture with the concave surface towards the film. This shortens the cameras, but focuses on a slightly curved film plane.

Actually, the field curvature is the same regardless of the orientation the lens. The Petzval field curvature of a simple lens depends only on the focal length of the lens and the refractive index of the glass. I don't remember the exact formula.

 

[alanrockwood]

What about measuring the magnification of the system using two or more point sources of light? I'll start by assuming two point sources in the object plane. Make sure one of the point sources is imaged at the center of the film. The other is imaged off-center, but not to far off center because you don't want the calculation be in error due to distortion of the image. Measure the distance between the center light source and the light source that is offset from the center. Then measure the distance between the corresponding points on the developed film. You also need to measure the distance from the light source to the lens. You should be able to calculate the focal length using ratios.

I'm doing some quick mental math here, but I think the formula you would use would be

X1/Y1=X2/Y2

where X1 is the distance from the lens to the center light source, Y1 is the distance from the center light source to second light source, X2 is the distance between the two points on the film plane, and Y2 is the focal length. The only unknown is Y2, so you measure the three other quantities and solve for Y2.

There are several ways for this scheme to go wrong, but I thought I would at least bring up the idea. For example, if the lens is position for best compromise focus then the scheme above may give slight errors if what you want is the focal length of the paraxial rays. On the other hand, maybe what you really want is the best-compromise focal length rather than the focal length of the paraxial ray.

Also there is the issue of principal planes, which has already been mentioned. I think errors due to not knowing the position of the principal planes can be minimized if you pick X1 to be large compared to the possible error in locating (i.e. guessing) the position of the principle plane for the object distance. If you just want the focal length and don't care about the exact location of the second principal plane then this should be good enough. If not good enough then by determining the optical focal length and seeing how that compares to the distance between the film plane at some reference point on the lens mount you should be able to locate the principle plane for the image relative to that reference point.

I mentioned that distortion can cause a problem with this scheme. One way to deal with this is to put several equally spaced point sources in a line. If there is no distortion then the image points should also be equally spaced. If the points are not equally spaced on the image plane then by using some judicious curve fitting you should be able to separate out the distortion term.

All of you optics experts out there please critique, or better yet suggest refinements, to the scheme I outlined above.

 

[shuddered]

I have a simple fixed focus and aperture box camera, with no data on it. I can measure the aperture and the shutter speed, I need the focal length. It has a single meniscus lens. I have measured the distance from the centre of the lens to the film plane and it is 46mm. I have then attempted to measure the focal length by using an optical bench and 1/F=1/U+1/V. Despite a deal of care and taking 16 measurements, I get a result of 52mm.

Now, as I understand it, the focal length must be equal to or LESS that the distance from the lens to the film (if you are focussed on infinity you focus nearer by moving the lens forward).

So what is happening - is 1/F=1/U+1/V not valid for meniscus lenses?

were you able to learn the focal length? can you post a photograph of the camera so if we run across the same on in ocean of box cameras we might know too?