# Multiple lenses systems - specific scenarios

1. Jul 2, 2012

### JYZero

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

Hi all... this isn't really a homework question, but more a question to reinforce the concept of multiple lenses. Firstly, it makes sense that the image location of an object would be behind a 2-convergent lenses system, provided they are sufficiently spaced apart.

However, in the case of a system where a convergent lens is followed by a divergent lens, OR a 2-divergent lenses system, I want to make sure that I understand what's happening to the image location.

2. Relevant equations

None ... I want to solve this qualitatively.

3. The attempt at a solution

In the case where a divergent lens follows the convergent lens .... assuming that the image that is produced by the first lens is real, the ultimate image ends up being somewhere between the first and second lens. It ends up being:

1) VIRTUAL, relative to the second lens
2) INVERTED, (negative magnification for 1st lenses, positive magnification for 2nd)
3) Reduced, enlarged, or not magnified in anyway, depending on the magnification of each of the individual lenses

Assuming that I am observing the object from the Real side, I would perceive the object to be between the 1st and second lens ... is this right?

The second scenario is a little harder for me to visualize. Based on the properties of divergent lens, the image would be virtual, upright and reduced. The first reduction is equivalent in magnitude to the magnification offered by the 1st lens, while another reduction is equivalent in magnitude to the magnification offered by the 2nd lens. I would also think that the virtual image created will be located between the 2 lenses, or between the 1st image and 1st lenses, depending on how the equation 1/f = 1/i + 1/o works out. Qualitatively, would this mean that, as an observer on the opposite side of the lenses system, I would perceive the object to be either between the 2 lenses OR behind both lenses?

However, I don't understand how the 1st image can act as an object for the 2nd lens, when that image (due to the 1st lens being divergent) ends up in front of the 1st lens. Will the 1st lens being "in the way" of the path between the 1st image and the 2nd lens alter the calculations in any way?

Lastly, if a virtual image can act as an object for a lens, can't the virtual image of the 1st lens act as an object on itself?

Last edited: Jul 2, 2012