# Finding focal length of the lens using "u-v" method

• I
• VVS2000
In summary: There's also Moire deflectometry, something I haven't tried but seems...similar to what you're describing?
VVS2000
I was just checking out this experiment for finding focal length of a lens that I did few years back. the method used was called as the u-v method(https://www.concepts-of-physics.com/pdf/uv-method.pdf), and here in this method, object distance u and image distance v is measured from the sharp edge of the lens and the lens is assumed to have zero thickness. If the lens does have thickness say "d", how would you measure u & v then? from the central bulge on the either side of the lens through which the optic axis passes through, or from the same sharp edge?

I would say to use the central line of a symmetrical convex lens rather than the edge.
The important thing is the refraction that happens at both convex surfaces of the lens.
Imagine that those surfaces are extended beyond the physical edges and converge at one point, like in the lens represented in the linked paper.

VVS2000
VVS2000 said:
I was just checking out this experiment for finding focal length of a lens that I did few years back. the method used was called as the u-v method(https://www.concepts-of-physics.com/pdf/uv-method.pdf), and here in this method, object distance u and image distance v is measured from the sharp edge of the lens and the lens is assumed to have zero thickness. If the lens does have thickness say "d", how would you measure u & v then? from the central bulge on the either side of the lens through which the optic axis passes through, or from the same sharp edge?
How accurately and with what precision do you need to determine the focal length?

VVS2000
VVS2000 and Lnewqban
Lnewqban said:
I would say to use the central line of a symmetrical convex lens rather than the edge.
The important thing is the refraction that happens at both convex surfaces of the lens.
Imagine that those surfaces are extended beyond the physical edges and converge at one point, like in the lens represented in the linked paper.
yeah I figured that would be it because we also measure the focal length along the central line as well

jtbell said:
If the lens has non-negligible thickness and you want to be precise, you have to use the principal planes of the lens. A Google search for "thick lens principal planes" produces many sites with details, for example:

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/priplan.html
yeah but experimentally I don't think you can use these principal planes as you don't know their position accurately

Andy Resnick said:
How accurately and with what precision do you need to determine the focal length?
That's a great question. Honestly I was just looking at these experiments that I did few years back and seeing this expt just made me think of how would this method hold for thick lenses. and since I learned a bit about aberrations in lenses, and these aberrations are on the orders of millimeters for a lens whose focal length in the range of centimeters, and using a single laser beam as our source at a certain height above the axis, it would be ideal to have our measured focal length within few millimetres of the expected focal length with the aberration factored into it

VVS2000 said:
That's a great question. Honestly I was just looking at these experiments that I did few years back and seeing this expt just made me think of how would this method hold for thick lenses. and since I learned a bit about aberrations in lenses, and these aberrations are on the orders of millimeters for a lens whose focal length in the range of centimeters, and using a single laser beam as our source at a certain height above the axis, it would be ideal to have our measured focal length within few millimetres of the expected focal length with the aberration factored into it

It sounds like you want to do some advanced-level measurements- quantifying the lens aberrations in addition to measuring the focal length, all to a precision and accuracy of a few percent. This requires some specialized setups, all requiring plane wave illumination of the optic under test.

The best way to measure the focal distance (as opposed to the back focal length) is by using a nodal slide bench:

https://opg.optica.org/josa/fulltext.cfm?uri=josa-22-4-207&id=48637

but there are other methods- for measuring the impact of aberrations on focal length, you could use something like a Hartmann-Shack wavefront test:

https://spotoptics.com/knowledge-corner/shack-hartmann-vs-hartmann-test/

There's also Moire deflectometry, something I haven't tried but seems interesting:

https://www.spiedigitallibrary.org/...o-Lens-Analysis/10.1117/12.951037.short?SSO=1

berkeman and VVS2000
Andy Resnick said:
It sounds like you want to do some advanced-level measurements- quantifying the lens aberrations in addition to measuring the focal length, all to a precision and accuracy of a few percent. This requires some specialized setups, all requiring plane wave illumination of the optic under test.

The best way to measure the focal distance (as opposed to the back focal length) is by using a nodal slide bench:

https://opg.optica.org/josa/fulltext.cfm?uri=josa-22-4-207&id=48637

but there are other methods- for measuring the impact of aberrations on focal length, you could use something like a Hartmann-Shack wavefront test:

https://spotoptics.com/knowledge-corner/shack-hartmann-vs-hartmann-test/

There's also Moire deflectometry, something I haven't tried but seems interesting:

https://www.spiedigitallibrary.org/...o-Lens-Analysis/10.1117/12.951037.short?SSO=1
No I don't want like practically test it but just thinking some ways of accurately arriving at a result. Thanks for the links, will definitely check them out

## 1. What is the "u-v" method for finding the focal length of a lens?

The "u-v" method is a technique used to find the focal length of a lens by measuring the distance between the object and the image formed by the lens. It involves using the lens formula, 1/u + 1/v = 1/f, where u is the object distance, v is the image distance, and f is the focal length.

## 2. What equipment is needed to perform the "u-v" method?

To perform the "u-v" method, you will need a lens, a light source, a screen or paper to project the image onto, and a ruler or measuring tape to measure the distances. A tripod or stand may also be helpful to keep the lens and screen in place.

## 3. How do you measure the object and image distances for the "u-v" method?

The object distance (u) is the distance between the object and the lens. This can be measured using a ruler or measuring tape. The image distance (v) is the distance between the lens and the image formed on the screen or paper. This can also be measured using a ruler or measuring tape.

## 4. Can the "u-v" method be used for all types of lenses?

Yes, the "u-v" method can be used for all types of lenses, including convex, concave, and combination lenses. However, it may be more accurate for lenses with a small focal length compared to those with a large focal length.

## 5. Are there any limitations or sources of error when using the "u-v" method?

One limitation of the "u-v" method is that it assumes the lens is thin, meaning the distance between the object and the lens is much larger than the thickness of the lens. If this is not the case, the results may be less accurate. Additionally, human error in measuring the distances can also lead to inaccuracies in the calculated focal length.

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