precisely measure focal length?

[Krutz]

pretty basic question, it seems.
i have 11 lenses (9 to 22mm diameter), plano-convex (or slightly concave), convex-convex, convex-concave, concave-concave. pretty much any combination it seems. found in an old scope and an industrial securitycam. i want to try to build a beamexpander from two of them. surely i wont find a good combination, but who knows?

how do i find out the focal length?

- looking through it, when does a thin line drawn on paper appear sharp? thats quite unprecise!

- shining a laser through it? when is the dot the smallest? around the focal length, the dot is so small i cant see much difference any more. and if the initial beam isnt perfectly collimated it will add to the error further..

- shining a laser through, measuring the (greatly enlarged) dot after one meter. tried this with a greenie. the dot has no defined edge (tem0! doh!) to measure. the beam isnt all collimated, it is maybe 1mm at the aperture, 2mm after one meter.no way to measure the divergence precisely!
made a table, tried to calculate the focal length:

(focalpoint to wall) (focallength)
-------------------------- = -------------------
(projected dot) (initial beamdiameter)


would then be:

(beam diameter) * (focalpoint to wall)
focallength = ----------------------------------------------------------
(projected dot) + (laserbeam)


for example, "lens 3" projects a 35mm dot after one meter (total!) distance. laserbeam is 1mm at aperture, 2mm at the 1m target. with that formula it would be a focallength of 54,1mm:

2 * 1000 / 35 + 2 = 54,1

thats totally off.
half of it, 27mm, fits better. but shining a laser directly through it, it seems to be a focal length of around 20mm?


ah well, its all guessing here, and not knowing. any hints? how to measure, or at least how to calculate? ..and what about those negative lenses.. *sigh*

how common would be a focal length of, say, 23mm, or even 23,7mm? would i assume its 24mm, in that case?

thank you a lot!

manuel

edit:
..how i got to that formula? uhm.. i drew a diagram, measured all distances, thought about how to formulate it, and searched for causalities. on the paper it all worked out with that formula. more precise than i could verify with a ruler.
will draw and post the setup if its not clear?

 

[HIMNL9]

The only precise way is use one lensmeter, like these ones (but actually are available 4-beams types that do all in automatic, and directly shows you all the data on a display)
Lensmeter - Wikipedia, the free encyclopedia

An empiric system, that is not extremely precise, but can give you an idea, is using a white plate (a desk or a paper foil on a desk), a cardboard plate with a hole in the middle (just for hold the lens and make a bit of shadow under it), and a ruler or caliper, and having a ceiling with a lampholder (also neons are ok)

Just put the lens on the cardboard plate, over the hole, staying right under the lampholder, and move it until you get on the white plate the more precise and focused image of the lampholder ..... the distance from the lens and the white plate is the focal lenght (more or less, cause the real focal lenght is to be measured from an infinite distance light source ..... but for the lenses that we usually use for lasers, that have FL of some millimeters, a lampholder at a pair of meters of distance is enough, for get a reasonable idea about the FL of a lens)

Ofcourse, this system only works with positive (magnifying) lenses .....

Using a laser, due to the intensity of the dot and small size of the source (and different divergences from different lasers, too), imho, is not the better way ..... your system can work with perfect lenses and zero millirads divergences of the beam, but ideal beams don't exists


Edit: there is also a different way, doing all in reverse ..... you need a diapositive (better if old types in glass, so don't bend), a light source (can be a diffused laser or a lamp under an opaline glass), and something for hold your lens ..... just put the diapositive in front of the light source, then the lens in front of it, and projec the image on a wall (2 or 3 meters away is enough) ..... when you see the image of the diapositive perfectly focused on the wall, the distance from the lens and the diapositive is your focal lenght

 

[lasersbee]

Yeah... that's exactly the way I check the focal length of
unknown lenses... a desk incandescent lamp and white surface
until image is focused crisp and sharp.
Then measure the distance between the lens and white surface...

You can also do it with the Sun... focusing it to the smallest "dot"...
but that usually ends in burning the measuring surface...

Jerry

 

[Krutz]

thanks for the comments!
i measured again, with a red laser, aixiz glass for a round beam. (de-)collimated to be 5mm at the aperture and at the target at 1m too. the calculated numbers are good, holding a lens at that distance focuses a laser as well as projects the image of my ceilinglamp sharp.
true, watching a projected image works better than i thought! precisely enough for +-1mm i guess.
my setup would be very precise, if i knew exactly the initial beamdiameter. a beam exactly 10mm wide and collimated (beamexpander!) would give precise numbers!

oh, wait, my calculator already gave me 8 digits numbers! thats precise!

manuel