Image Formed by a System of Lenses

In summary, the conversation revolved around solving a problem involving three converging lenses with a spacing of 2.2 cm between them. The lenses were used to image an insect 2.3 cm away. The equation 1/do + 1/di = 1/f was used to find the location of the image formed by each lens. The correct answer was 0.43 cm to the right of the third lens. The mistake in the calculation was using a positive value for the object distance with lens 3 when it should have been negative. Once this error was corrected, the correct answer was obtained.
  • #1
Renaldo
58
0

Homework Statement



Three converging lenses of focal length 2.5 cm are arranged with a spacing of 2.2 cm between them, and are used to image an insect 2.3 cm away. Where is the image?

Homework Equations



1/do + 1/di = 1/f

The Attempt at a Solution



I used the above equation to find the location formed by the first lens. Then I used that information to calculate the position of the image formed by the second lens. Finally, I used that information to calculate the position of the image formed by the third lens.

My answer is 0.66 cm to the right of the third lens.

I assumed the insect was initially to the right of the system of lenses.

Correct answer is 0.43 cm. What did I do wrong?
 
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  • #2
Renaldo said:

Homework Statement



Three converging lenses of focal length 2.5 cm are arranged with a spacing of 2.2 cm between them, and are used to image an insect 2.3 cm away. Where is the image?

Homework Equations



1/do + 1/di = 1/f

The Attempt at a Solution



I used the above equation to find the location formed by the first lens. Then I used that information to calculate the position of the image formed by the second lens. Finally, I used that information to calculate the position of the image formed by the third lens.

My answer is 0.66 cm to the right of the third lens.

I assumed the insect was initially to the right of the system of lenses.

Correct answer is 0.43 cm. What did I do wrong?
It's very hard to say what you did wrong unless you give us more detail.

What position did you get for the image from each lens ?
 
  • #3
I attached my work for this problem. db is the distance from the first first lens to the bug. The arrow represents the bug.
 

Attachments

  • Bug Optics.jpg
    Bug Optics.jpg
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  • #4
The image formed by the second lens is about 2.72 cm to the left of the second lens, thus about 5.2 cm to the right of the third lens.

[STRIKE]What sign should you use for 5.2 cm when used as the object distance with lens 3 ?[/STRIKE]

Added in Edit:

That should be
... thus about 0.52 cm to the left of the third lens.​

What sign should you use for 0.52 cm when used as the object distance with lens 3 ?
 
Last edited:
  • #5
I just want to make sure we are using the same convention.

My L1 is on the far right. L3 is on the far left. L2 is in between. If the image formed by the second lens is 2.72 cm to the left of the second lens, then it would not be 5.2 cm to the right of the third lens. Rather, it would be 0.52 cm to the left of the third lens.
 
  • #6
Renaldo said:
I just want to make sure we are using the same convention.

My L1 is on the far right. L3 is on the far left. L2 is in between. If the image formed by the second lens is 2.72 cm to the left of the second lens, then it would not be 5.2 cm to the right of the third lens. Rather, it would be 0.52 cm to the left of the third lens.
Right. Those were errors -- a typo and a dyslexia error.

That should have said:
The image formed by the second lens is about 2.72 cm to the left of the second lens, thus about 0.52 cm to the left of the third lens.​


The important question is:
What sign should you use for the object distance with lens 3 if the object is to the left of the lens ?​
 
  • #7
negative, because the image is formed on the same side as the object.
 
  • #8
Renaldo said:
negative, because the image is formed on the same side as the object.
Correct.

That should give you the desired result for the location of the final image.
 
  • #9
At first I said the image was to the right of the third lens. I now realize that was incorrect. I still don't understand how that affects the numerical value of my final answer, which is still wrong.
 
  • #10
Show your numbers.

It works out for me.
 
  • #11
1/f = 0.4
1/do = 1.923

1/(0.4 - 1.923) = -0.66 cm

(f = 2.5)
(do = 0.52)
 
Last edited:
  • #12
Renaldo said:
1/f = 0.4
1/do = 1.923

1/(0.4 - 1.923) = -0.66 cm

(f = 2.5)
(do = 0.52)
dO is negative.

[itex]\displaystyle \frac{1}{d_i}+\frac{1}{\displaystyle-\frac{2957}{5690}}=\frac{1}{2.5}[/itex]

This gives approximately
##\displaystyle d_i=\frac{1}{0.4+1.9242} ##​
 
  • #13
Thanks. That works.
 

Related to Image Formed by a System of Lenses

1. How does a system of lenses form an image?

When light passes through a system of lenses, it is refracted and bent in different directions. The lenses work together to converge or diverge the light rays, ultimately forming an image. The type of image formed depends on the configuration and properties of the lenses.

2. What factors affect the formation of an image by a system of lenses?

The factors that affect the image formed by a system of lenses include the curvature and thickness of the lenses, the distance between the lenses, and the properties of the material the lenses are made of. The distance of the object from the lenses and the distance of the image from the lenses also play a role in the formation of the image.

3. Can a system of lenses produce different types of images?

Yes, a system of lenses can produce different types of images depending on the configuration of the lenses. For example, a convex lens can produce a real or virtual image, while a concave lens can only produce a virtual image. By combining different types of lenses, it is possible to create a variety of images.

4. How does the position of an object affect the image formed by a system of lenses?

The position of the object in relation to the lenses can affect the size and orientation of the image formed. If the object is placed close to the lenses, the image will be larger compared to if the object is placed further away. Additionally, the orientation of the image can be inverted or upright depending on the distance and configuration of the lenses.

5. What is the difference between a real and virtual image formed by a system of lenses?

A real image is formed when light rays actually converge at a point to form an image that can be projected onto a screen. This type of image can be captured by a camera or seen by the naked eye. On the other hand, a virtual image is formed when light rays appear to be coming from a specific point but do not actually converge. This type of image cannot be projected onto a screen and can only be seen through the lenses.

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