Question regarding a two-lens system

In summary, when two converging lenses with focal length of 15 cm are placed 20 cm apart, an object placed 30 cm in front of the first lens will result in a final image distance of 30 cm and a magnification of 1. The image formed by the first lens will serve as the object for the second lens, resulting in a final image behind the second lens.
  • #1
pisquared
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Homework Statement


Two converging lenses, each of focal length 15 cm, are placed 20 cm apart, and an object is placed 30 cm in front of the first. Where is the final image formed and what is the magnification of the system?

Homework Equations


Mtot = M1 * M2
(1/f) = 1/do + 1/di

The Attempt at a Solution


[/B]
Okay, I was able to find the image distance would be 30 cm, but I have no idea how that would happen if the lenses are 20 cm apart. When drawing the ray diagram, the rays touch the second lens before converging, so I don't know where to go from there. Any help would be appreciated. Thanks!
 
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  • #2
pisquared said:

Homework Statement


Two converging lenses, each of focal length 15 cm, are placed 20 cm apart, and an object is placed 30 cm in front of the first. Where is the final image formed and what is the magnification of the system?

Homework Equations


Mtot = M1 * M2
(1/f) = 1/do + 1/di

The Attempt at a Solution


[/B]
Okay, I was able to find the image distance would be 30 cm, but I have no idea how that would happen if the lenses are 20 cm apart. When drawing the ray diagram, the rays touch the second lens before converging, so I don't know where to go from there. Any help would be appreciated. Thanks!
One way is to take the image that would be formed by the first lens and treat it as the source object for the second lens. You just have to be careful about which side the final image will be.
 
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  • #3
pisquared said:
Okay, I was able to find the image distance would be 30 cm, but I have no idea how that would happen if the lenses are 20 cm apart. When drawing the ray diagram, the rays touch the second lens before converging, so I don't know where to go from there.
You can take that image as object of the second lens. As it is behind the second lens, take the object distance negative.
 
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  • #4
@ehild @haruspex So the first image would go straight through the second lens and be 10 cm behind it, then be the object of the second lens?
 
  • #5
pisquared said:
@ehild @haruspex So the first image would go straight through the second lens and be 10 cm behind it, then be the object of the second lens?
Yes.
 

Related to Question regarding a two-lens system

1. How does a two-lens system work?

A two-lens system consists of two lenses placed in close proximity to one another, with the first lens (known as the objective lens) focusing the incoming light onto the second lens (known as the eyepiece lens). The eyepiece lens then magnifies the image produced by the objective lens, allowing the viewer to see a larger and clearer image.

2. What is the purpose of using a two-lens system?

A two-lens system is often used in optical devices such as microscopes and telescopes to magnify and enhance the clarity of the image being viewed. It allows for a greater level of detail to be seen and can improve the overall viewing experience.

3. How do the two lenses in a two-lens system differ?

The two lenses in a two-lens system differ in terms of their focal length and shape. The objective lens typically has a shorter focal length and a larger diameter, while the eyepiece lens has a longer focal length and a smaller diameter. This difference in shape and focal length allows for the magnification and clarity of the image.

4. Can a two-lens system be adjusted?

Yes, a two-lens system can be adjusted by changing the distance between the two lenses. This can be done manually by adjusting the focus knob on the optical device, or automatically in some advanced systems. Adjusting the distance between the lenses can change the magnification and focus of the image being viewed.

5. Are there any limitations to a two-lens system?

While a two-lens system can greatly enhance the viewing experience, it does have some limitations. The magnification and clarity of the image are limited by the quality and design of the lenses, as well as the distance between them. Additionally, the two-lens system may not be effective in situations where there is extreme curvature of light, such as in very thick or curved lenses.

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