How Do You Calculate Image Distance with Multiple Lenses?

In summary, to find the distance from the first mirror, you can use the thin lens equation and the distances from the first and second lenses to the image.
  • #1
majormaaz
62
1

Homework Statement


Two lenses that are L = 34 cm apart are used to form an image, as shown in figure. Lens 1 is converging and has a focal length f1 = 13 cm; lens 2 is diverging and has a focal length f2 = -7.0 cm.
I am supposed to find out the distance from the first mirror
http://www.webassign.net/walker/26-52alt.gif

Homework Equations


I know how to solve problems with one lens/mirror, but I'm not sure if you have to draw out the rays and extend them to the second lens/mirror to solve it.

The Attempt at a Solution


As I said earlier, I am guessing that drawing out the lines will solve it, but now I'm wondering if there is an equation for it.
 
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  • #2


Hello, thank you for your question. You are correct in thinking that drawing out the rays can help you solve this problem. In order to find the distance from the first mirror, you can use the thin lens equation: 1/f = 1/di + 1/do, where f is the focal length of the lens, di is the distance from the image to the lens, and do is the distance from the object to the lens.

For this problem, we can start by finding the distance from the first lens to the image, which we can call di1. We can use the thin lens equation with f1 = 13 cm and di1 = -21 cm (since the image is formed 21 cm to the left of the first lens). This gives us 1/13 = 1/-21 + 1/do, which simplifies to do = -273 cm.

Next, we can use the same equation to find the distance from the second lens to the image, which we can call di2. This time, we use f2 = -7.0 cm and di2 = L - do = 34 - (-273) = 307 cm (since the image is formed 307 cm to the right of the second lens). This gives us 1/-7.0 = 1/307 + 1/do, which simplifies to do = 49 cm.

Finally, to find the distance from the first mirror, we can use the fact that the distance from the first mirror to the first lens is 34 cm. Therefore, the distance from the first mirror to the image is 34 cm + do = 34 cm + 49 cm = 83 cm.

I hope this helps! Let me know if you have any further questions.
 

Related to How Do You Calculate Image Distance with Multiple Lenses?

1. How can two mirrors and lenses be used to create a magnified image?

Two mirrors and lenses can be arranged in a specific way to create a magnified image. One mirror is placed in front of the object, reflecting the light towards the second mirror. The second mirror then reflects the light towards the lens, which refracts the light and creates a magnified image of the object.

2. What is the difference between convex and concave lenses?

Convex lenses are thicker in the middle and thinner at the edges, causing light rays to converge and creating a magnified image. Concave lenses are thinner in the middle and thicker at the edges, causing light rays to diverge and creating a smaller, virtual image.

3. How does the distance between the two mirrors affect the resulting image?

The distance between the two mirrors affects the size and orientation of the resulting image. A larger distance will create a smaller, inverted image, while a smaller distance will create a larger, inverted image. If the distance is too small, the mirrors may not be able to reflect the light properly and no image will be formed.

4. Can two convex lenses be used to create a magnified image?

Yes, two convex lenses can be used to create a magnified image. The first lens will create a magnified image of the object, and the second lens will further magnify the image. This is known as a compound lens system.

5. How can the position of the object affect the resulting image in a two mirrors and lenses problem?

The position of the object can affect the resulting image in a few ways. If the object is placed between the two mirrors, a larger distance between the mirrors will create a smaller, inverted image. If the object is placed beyond the focal point of the lens, a larger distance between the mirrors will create a larger, inverted image. If the object is placed at the focal point of the lens, no image will be formed.

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