# Homework Help: Optics Lab: Combined Lens Systems

1. Nov 11, 2014

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
1/f=1/f1 + 1/f2 - d/(1/f1 *1/f2 )

3. 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

2. Nov 12, 2014

### 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.

Last edited: Nov 12, 2014
3. Nov 12, 2014

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?

4. Nov 13, 2014

### 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.