Multiple lenses systems - specific scenarios

In summary, the conversation discusses the concept of multiple lenses and how the image location is affected in different scenarios. It explains that in the case of a convergent lens followed by a divergent lens, the final image will be virtual, inverted, and located between the two lenses. In the second scenario, the final image will be virtual, upright, and reduced, and it could be located either between the two lenses or behind both lenses. The conversation also clarifies how the first image can act as an object for the second lens, and the possibility of a virtual image acting as an object for a lens.
  • #1
JYZero
3
0

Homework Statement



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.

Homework Equations



None ... I want to solve this qualitatively.

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?

Thanks in advance!
 
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  • #2


Hello! Thank you for your question. You are correct in your understanding that in the case of a convergent lens followed by a divergent lens, the final image will be virtual, inverted, and located between the two lenses. This is because the first lens focuses the light rays and creates a real image, which then acts as the object for the second lens. The second lens then diverges the light rays, creating a virtual image behind it.

In terms of the second scenario, your understanding is also correct. The final image will be virtual, upright, and reduced, and it will be located either between the two lenses or behind both lenses, depending on the specific parameters of the lenses and the distance between them. The equation 1/f = 1/i + 1/o will still hold true, as it takes into account the effects of both lenses on the light rays.

As for your question about the first image acting as an object for the second lens, it is important to note that the first image is not physically located in front of the first lens. It is a virtual image, meaning that the light rays do not actually converge at that point. Therefore, the first lens is not "in the way" of the light rays between the first image and the second lens. The calculations will not be altered in any way.

And yes, a virtual image can act as an object for a lens. This is because the light rays from the virtual image behave in the same way as light rays from a real object, and can therefore be focused or diverged by a lens. This is also why the virtual image of the first lens can act as an object for the second lens.

I hope this helps clarify things for you. Let me know if you have any further questions. Happy experimenting!
 

1. How do multiple lenses affect the overall performance of a system?

Multiple lenses can greatly improve the performance of a system by allowing for a wider range of magnifications and better control of aberrations. However, if the lenses are not properly aligned or have different optical properties, they can also introduce distortions and reduce the overall performance.

2. What is the difference between a simple lens and a compound lens system?

A simple lens consists of only one lens element, while a compound lens system consists of multiple lens elements that work together to achieve a desired optical function. Compound lenses are often used to correct for aberrations and improve image quality in comparison to simple lenses.

3. How do you calculate the focal length of a multiple lens system?

The focal length of a multiple lens system can be calculated using the lens maker's formula, which takes into account the individual focal lengths and distances between the lens elements. It is important to note that the focal length of a compound lens system will be different from the individual focal lengths of its components.

4. What are some common applications of multiple lens systems?

Multiple lens systems are commonly used in photography, microscopy, telescopes, and eyeglasses. They can also be found in various optical instruments, such as projectors, lasers, and binoculars.

5. How do you troubleshoot problems with a multiple lens system?

If a multiple lens system is not performing as expected, it is important to check for proper alignment and cleaning of the lenses. Other factors that can affect performance include incorrect focal length calculations, damaged or misaligned lens elements, and environmental factors such as temperature and humidity. Consulting an expert or following specific troubleshooting procedures can help identify and solve any issues with a multiple lens system.

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