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

• I
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?

Homework Helper
Gold Member
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
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
Mentor
• VVS2000 and Lnewqban
VVS2000
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

VVS2000
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

VVS2000
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

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
VVS2000
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