Optics Lab: Combined Lens Systems

[NotMad]

Homework Statement

Given a system composed of a convergent lens and divergent lens (separation d between), how do I best calculate the focal length of the divergent lens?

What is the best way to set up the system (converging lens first? diverging lens first?). There is plenty of documentation regarding the relevant equations, but I have had trouble locating a clear description of how to actually do any of the experimental work.

What measurements are relevant? How do I measure the focal length of the system?

I'm pretty lost here and I've been thinking about this for a while >.<

Homework Equations

1/f=1/f₁ + 1/f₂ - d/(1/f₁ *1/f₂ )

The Attempt at a Solution

My current setup is object -> converging lens (known focal length) -> diverging lens (unknown focal length) -> screen.

I've taken the distance from the object to the first lens, then from the second lens to the image and attempted to use this to solve for the focal length of the system, but I do not know if this is correct.

I have considered using the distance from the image produced by the converging lens to the diverging lens since the diverging lens picks up the converging lens's image. I think this may be the right path, but I am again unsure.

I have no way to check if the focal lengths are correct.

Cheers
NM

 

[andrevdh]

First locate the image of converging lens with the screen.
This image will then be used as the object for the divergent lens which you can then
place on the optical bench so that the object (the previous image) is to
the right-hand side of the diverging lens. Its object distance will thus
be negative since it is a virtual object. Now move the divergent lens around
until you can see the image formed by the divergent lens on the screen (it will be further away
than the previous image since the divergent lens opens up the rays a bit). You can then use the thin lens formula to calculate the focal length of the divergent lens. Repeat moving the divergent lens to a
different position, recalculate and average the focal lengths. You can also draw
a graph of the inverse of the image distance versus the inverse of the object distance
from which you can determine the focal length.

 

[NotMad]

First locate the image of converging lens with the screen.
This image will then be used as the object for the divergent lens which you can then
place on the optical bench so that the object (the previous image) is to
the right-hand side of the diverging lens. Its object distance will thus
be negative since it is a virtual object. Now move the divergent lens around
until you can see the image formed by the divergent lens on the screen (it will be further away
than the previous image since the divergent lens opens up the rays a bit). You can then use the thin lens formula to calculate the focal length of the divergent lens. Repeat moving the divergent lens to a
different position, recalculate and average the focal lengths. You can also draw
a graph of the inverse of the image distance versus the inverse of the object distance
from which you can determine the focal length.

Thank you for taking the time to reply, andre, but I'm afraid this is all of the information I could extract from my own search. What, in fact, are the image an object distances? From where do I measure them?

 

[andrevdh]

The object distance is the distance from the lens to whatever you are using
to form an image of, usually it is something that emits a lot of light. You would
start out by positioning the converging lens at some distance from this bright
object. Then you would move a screen around on the other side of the lens to
find the position of the screen where a sharp image of the bright object is observed
on the screen. The image distance is then the distance from the lens to the screen.
Not all object distances will produce an image though. The object needs to be
further than a certain minimum distance from the lens to produce an image. This
minimum object distance at which the converging lens will produce a real image
(one that can be seen on a screen) is the focal length of the lens.

 

[HalfLostAndSearching]

Dear student,

Thank you for reaching out with your question. I understand the importance of clear experimental procedures and accurate measurements in conducting research. Here are some suggestions to help you with your optics lab and calculating the focal length of the diverging lens.

Firstly, it is important to have a clear understanding of the setup and the relevant equations before starting the experiment. Based on your description, it seems like you have a basic understanding of the setup and the relevant equation (1/f=1/f1 + 1/f2 - d/(1/f1 *1/f2 )).

To accurately measure the focal length of the diverging lens, it is best to set up the system with the converging lens first, followed by the diverging lens. This is because the converging lens will produce a real image, which can then be used as the object for the diverging lens. This will make the measurements more accurate and eliminate any errors caused by the position of the object.

In terms of measurements, the relevant ones would be the distance between the two lenses (d), the distance between the object and the first lens, and the distance between the second lens and the image produced by the converging lens. These measurements can then be used in the equation (1/f=1/f1 + 1/f2 - d/(1/f1 *1/f2 )) to solve for the focal length of the diverging lens.

To check the accuracy of your measurements, you can use a known focal length for the converging lens and compare it to the focal length you calculate for the diverging lens. This will help you identify any errors in your measurements and make any necessary adjustments.

I hope this helps and I wish you success in your experiment. Remember to always double-check your setup and measurements to ensure accurate results. Good luck!