Reason for Different Focus Distances in Converging Lens Lab

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SUMMARY

The forum discussion centers on the discrepancies in focal lengths measured using a converging lens in two different setups: one with a distant tree (15 cm) and another with a candle on an optics bench (16.3 cm). Participants highlight measurement errors and lens aberrations, particularly astigmatism and chromatic aberration, as potential causes for the differences. The discussion emphasizes the importance of error analysis, suggesting that repeated measurements can help clarify the accuracy of results and identify procedural errors.

PREREQUISITES
  • Understanding of converging lens principles
  • Familiarity with measurement techniques in optics
  • Knowledge of lens aberrations, specifically astigmatism and chromatic aberration
  • Basic concepts of error analysis in experimental physics
NEXT STEPS
  • Conduct experiments to measure focal lengths using both a distant object and a nearby candle
  • Learn about "thick lens" equations and their applications
  • Explore methods for performing error analysis in optical experiments
  • Investigate the effects of lens rotation on focal length measurements
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Students and educators in physics, optical engineers, and anyone interested in understanding the principles of lens behavior and measurement accuracy in optical experiments.

jnimagine
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we used a converging lens and a screen with white paper in front of a window to form an image of a distant tree outside. This was about 15cm.
When we used an optics bench and a candle to figure out the focus, it was 16.3cm... What would be a reason for the difference in the number?
 
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First -- do you have errors associated with your measurements? Figure out your errors and then you might find out that your answers really "agree."

Then if you still have trouble -- you might get think about various types of lens aberrations and see if you could figure out how to check those things.
 
physics girl phd said:
First -- do you have errors associated with your measurements? Figure out your errors and then you might find out that your answers really "agree."

Then if you still have trouble -- you might get think about various types of lens aberrations and see if you could figure out how to check those things.

well I'm sure there were errors in measuring the image distance... we might have not measured the sharpest image and just measuring with the ruler might not have been too accurate... what sort of lens aberrations would cause this? even if there were aberrations, it doesn't explain Why the the focal length measured outside is different from the focal length measured with optics bench. It only explains that both weren't that accurate...
 
Are you familiar at all with simple "error analysis"? If your answer of one method is 15(+/-2)cm and the other is 16.3(+/-0.5) do you answer "disagree"?

Then this seemed to be a good website regarding aberrations:
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/aberrcon.html
I could instantly think of one type that might give you this result... can you find it?

EDIT: hint... many people's eyesight suffers from this type of aberration, including mine.
 
Last edited:
physics girl phd said:
Are you familiar at all with simple "error analysis"? If your answer of one method is 15(+/-2)cm and the other is 16.3(+/-0.5) do you answer "disagree"?

Then this seemed to be a good website regarding aberrations:
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/aberrcon.html
I could instantly think of one type that might give you this result... can you find it?

EDIT: hint... many people's eyesight suffers from this type of aberration, including mine.

no... I'm not familiar with the error analysis...
and is it astigmatism that caused the difference? or chromatic? :confused: a little help please? T.T
 
Chromatic aberrations have to do with color. Do you think color had an effect?

Astigmatism has to do with different axes on the lens (say the x-axis and y-aixis if your optic axis is along z). Do you think color had an effect?

How could you experiment to check these two possibilities?

BTW , I think you're narrowing in on the one I thought might be a good possibility. :biggrin:
 
physics girl phd said:
Chromatic aberrations have to do with color. Do you think color had an effect?

Astigmatism has to do with different axes on the lens (say the x-axis and y-aixis if your optic axis is along z). Do you think color had an effect?

How could you experiment to check these two possibilities?

BTW , I think you're narrowing in on the one I thought might be a good possibility. :biggrin:

is it astigmatism...? but i used the same lenses for both... then the focal length should be the same... chromatic... when we focused a distant tree, it had more colours than the candle... the different colour of rays refract differently...hmmm... this is hard.. :redface:
 
If I had to guess... I'd think assigmatism. If you ROTATE the lens, then you might get different measured values. You could check this by putting a small marker tick on the rim of the lens... and seeing if the focus changes as you rotate the lens in both experiments.

There might also be some procedural error in how one experiment was sone over the other... but hopefully that gets covered in the error estimates. The error analysis just might say one technique had more error in the measurement than the other, so the answers really do agree (hey -- you didn't get 100cm for one method...15cm and 16.3cm are at least pretty close).
 
physics girl phd said:
If I had to guess... I'd think assigmatism. If you ROTATE the lens, then you might get different measured values. You could check this by putting a small marker tick on the rim of the lens... and seeing if the focus changes as you rotate the lens in both experiments.

There might also be some procedural error in how one experiment was sone over the other... but hopefully that gets covered in the error estimates. The error analysis just might say one technique had more error in the measurement than the other, so the answers really do agree (hey -- you didn't get 100cm for one method...15cm and 16.3cm are at least pretty close).

but the lens we used was in a frame and so it was always in the same position when we used it with the optics bench as well... we never rotated it or anything...
 
  • #10
That's REALLY good that you noticed the frame! :biggrin: You know then that it probably isn't astigmatism (which is pretty common -- my eyes would focus a vertical line at a different focus than a horizontal line, because the curvature of my eye is different for those two directions :bugeye:). But unless the len is really sloppy in your frame, you looked at the tree in the same orientation as the candle... excellent!

I personally also lean towards counting out chromatic aberation... you didn't notice the image of the tree LOOKING some funny color (like a bit too blue or yellow), did you? I think based on this, that there were probably just errors in measurements that you need to think about. So we'll talk about "error" more... :wink:

To get a good idea of how much your measurements have error, go back and do the two experiments again with the same lens and (even hopefully the same meter stick) -- but doing ALL the measurements of length, height, etc. without looking at all at your previous work. Then when you find the new results -- What is the average of the two tree experiments compared to the average of the two candle experiments? Are the averages closer than the initial two measurements? What if after this you go back and do it a third time... are the averages getting even closer? This type of error from measurement to measurement is probably best classified as "statistical error"... so doing the experiment a few times and averaging the results is better than just doing it once.

However, there is another type of error probably best known as "procedural error." If your averages aren't getting closer ("converging") then this is probably the case. This would happen, say if someone cut a centimeter off your meter stick, you didn't notice, and this changed the results of the two methods differently (this would maybe be called "machine error" because the measurement machine isn't working right, so you need to fix it by relabeling the numbers on the stick or getting a new stick. Other procedural errors would include human errors like analyzing the data wrong in some way. Did you somehow read the meter stick wrong, maybe using inches for some measurements and cm for others if both are marked on the stick? Or -- Is your lens really thick? That would mean that the common "thin lens" equations you are probably using wouldn't really describe your experimental data. You might need to look up "thick lens" equations.
 
  • #11
Chromatic abberation might be a good guess since the color distribution of a tree (leaning towards the short wavelengths) and a candle flame (more towards longer wavelengths - red do differ a lot. Did you use a distant tree? In that case the rays were all traveling close to the optical axis, which most like were not the case with the flame if it was close to the lens. All this is speculation though one would only know for sure by performing some more experimental investigations.
 
  • #12
physics girl phd said:
I personally also lean towards counting out chromatic aberation... you didn't notice the image of the tree LOOKING some funny color (like a bit too blue or yellow), did you? I think based on this, that there were probably just errors in measurements that you need to think about. So we'll talk about "error" more... :wink:

well... now that i think of it... the image of the tree was a bit yellow... it definitely wasn't the colour of the actual tree... i just thought it'd be a bit yellow because of the sunlight or somethin...
 
  • #13
Ooooh -- this gets fun -- now when you take the measurements again you can also see if changing the position of the lens slightly makes an image that is a bit blue... maybe by looking at the explanation of the abberations link we looked at earlier you could even predict what direction that might be... good luck with all your investigations... I'm sure you'll figure this interesting question out with a bit more experimentation!
 

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