Simple Optics: Image Formed By Two 15cm Lenses

  • Thread starter beethoven'smahomeboy
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In summary, the object placed at a distance of 15 cm from a converging lens with a focal length of 15 cm will form an image at infinity. When a second positive lens with the same focal length is placed 20 cm away from the first lens, the final image will be formed at the second lens's focal point, which is the same size as the original object. The distance between the two lenses is not a factor in determining the final image location.
  • #1
beethoven'smahomeboy
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An object is 15 cm from a converging lens of focal length 15 cm. A second positive lens of focal length 15 cm is 20 cm from the first lens. Where is the final image (s)?

Since 1/15+1/s=1/15 by the thin-lens equation, is there an image formed?
 
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  • #2
beethoven'smahomeboy,
If light from a far away object (parallel light rays) falls on a convex lens it will form an image of the object in it's focal plane (that is how the focal length of such a lens is defined). If an object is placed at the focus of a lens we get conversely that it forms an image of the object at infinity (very far away) again with parallel light rays leaving the lens. Your equation above get 1/s as zero, which implies that the image is at infinity. For the second lens the light looks like it is coming from an far away object (that is the rays are traveling parallel to each other after leaving the first lens). This means that the second lens will form an image of the original object at it's second focus. The distance between the two lenses are irrelevant. The object is therefore mapped from the focal point of the first lens to that of the second lens. Since both lenses have the same focal length the final image will be the same size as the original.
 
  • #3


Based on the given information, it appears that there will be a final image formed by the two 15 cm lenses. The first lens, with a focal length of 15 cm, will converge the light from the object and form an image at a distance of 15 cm from the lens. This image will then serve as the object for the second lens, which is placed 20 cm from the first lens. Using the thin-lens equation, we can calculate that the final image will be formed at a distance of 30 cm from the second lens. Therefore, there will indeed be a final image formed by the two lenses, located at a distance of 30 cm from the second lens.
 

1. How is an image formed by two 15cm lenses?

An image is formed by two 15cm lenses through a process called refraction. When light rays pass through the first lens, they are bent and converge at a focal point. This point becomes the object for the second lens, which then refracts the light rays again and forms an image at a further distance. The final image is a magnified and inverted version of the original object.

2. What is the relationship between the distance of the lenses and the image formed?

The distance between the two lenses, also known as the lens separation, determines the size and orientation of the final image. The larger the lens separation, the larger the image will be. However, if the lens separation is too small, the image will be distorted or not formed at all.

3. What happens if the lenses are placed too close together?

If the lenses are placed too close together, the light rays will not have enough space to converge and form a clear image. This can result in a blurred or distorted image. It is important to maintain an appropriate lens separation for the best image formation.

4. Can the focal length of the lenses affect the image formed?

Yes, the focal length of the lenses can affect the image formed. A longer focal length will result in a larger magnification of the image, while a shorter focal length will result in a smaller magnification. Additionally, the focal length also determines the distance at which the image is formed from the lenses.

5. What are the limitations of using two 15cm lenses to form an image?

One limitation of using two 15cm lenses to form an image is that the image will have a limited field of view. This means that the image will only be able to capture a small portion of the object being viewed. Additionally, the image may also have some distortion or aberrations due to the curvature of the lenses, which can affect the accuracy of the image.

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