1. An object at infinity (or rather, very, very far away) is viewed through two consecutive nses. The first lens through which the light passes is a diverging lens with a focal length -1.6 m. The position of the image seen through both lenses combined is the same as the osition of the first lens. The image viewed through just the first lens differs in size from e image viewed through both lenses such that one of these images is 3 times larger than Le other. image seen through both lenses object is far away HI diverging second lens lens d Is the final image upright or inverted, compared to the object's orientation? Explain. Determine whether the second lens needs to be converging or diverging, or whether both types of lenses are possible under the right conditions. Explain.

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter26: Image Formation By Mirrors And Lenses
Section: Chapter Questions
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### Optical System with Two Lenses

An object at infinity (or rather, very, very far away) is viewed through two consecutive lenses. The first lens through which the light passes is a diverging lens with a focal length of \(-1.6 \, \text{m}\). The position of the image seen through both lenses combined is the same as the position of the first lens. The image viewed through just the first lens differs in size from the image viewed through both lenses such that one of these images is three times larger than the other.

#### Diagram Explanation

The diagram shows two lenses aligned along the optical axis:

1. **Diverging Lens**: On the left, labeled as having a focal length of \(-1.6 \, \text{m}\). An object positioned at infinity on the left of this lens produces an image on its right.

2. **Second Lens**: Positioned at a distance \( x \) to the right of the diverging lens. The nature of this lens is not specified initially.

3. **Image Path and Size**: 
   - The object, indicated to be very far away, is represented with rays diverging into the first lens.
   - After passing through both lenses, the image location coincides with the position of the diverging lens, and its magnification is three times different compared to the first image formed by the diverging lens alone.

### Questions

**a.** Is the final image upright or inverted, compared to the object's orientation? Explain.

**b.** Determine whether the second lens needs to be converging or diverging, or whether both types of lenses are possible under the right conditions. Explain.

**c.** Find the distance that the lenses are separated.

**d.** Find the focal length of the second lens.
Transcribed Image Text:### Optical System with Two Lenses An object at infinity (or rather, very, very far away) is viewed through two consecutive lenses. The first lens through which the light passes is a diverging lens with a focal length of \(-1.6 \, \text{m}\). The position of the image seen through both lenses combined is the same as the position of the first lens. The image viewed through just the first lens differs in size from the image viewed through both lenses such that one of these images is three times larger than the other. #### Diagram Explanation The diagram shows two lenses aligned along the optical axis: 1. **Diverging Lens**: On the left, labeled as having a focal length of \(-1.6 \, \text{m}\). An object positioned at infinity on the left of this lens produces an image on its right. 2. **Second Lens**: Positioned at a distance \( x \) to the right of the diverging lens. The nature of this lens is not specified initially. 3. **Image Path and Size**: - The object, indicated to be very far away, is represented with rays diverging into the first lens. - After passing through both lenses, the image location coincides with the position of the diverging lens, and its magnification is three times different compared to the first image formed by the diverging lens alone. ### Questions **a.** Is the final image upright or inverted, compared to the object's orientation? Explain. **b.** Determine whether the second lens needs to be converging or diverging, or whether both types of lenses are possible under the right conditions. Explain. **c.** Find the distance that the lenses are separated. **d.** Find the focal length of the second lens.
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