Two converging lenses having focal lengths of  f1 = 11.2 cm and  f2 = 20.0 cm are placed  d = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position  x = 31.3 cm indicated. On the left, an arrow originating from a long horizontal line points upward and is labeled "Object." A vertical, convex lens, labeled "f1," is centered upon the horizontal line and is positioned a distance p to the right of the Object arrow. A second vertical, convex lens, labeled "f2," is positioned a distance d to the right of the left lens, and is also centered upon the horizontal line. A second arrow, labeled "Final image," lies between the two lenses at a distance x from the left lens, originates from the horizontal line, and points downward.

Physics for Scientists and Engineers
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Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter35: Image Fonnation
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Two converging lenses having focal lengths of  f1 = 11.2 cm and  f2 = 20.0 cm are placed  d = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position  x = 31.3 cm indicated.

On the left, an arrow originating from a long horizontal line points upward and is labeled "Object." A vertical, convex lens, labeled "f1," is centered upon the horizontal line and is positioned a distance p to the right of the Object arrow. A second vertical, convex lens, labeled "f2," is positioned a distance d to the right of the left lens, and is also centered upon the horizontal line. A second arrow, labeled "Final image," lies between the two lenses at a distance x from the left lens, originates from the horizontal line, and points downward.

 

**Title: Optical System Analysis with Converging Lenses**

**Overview:**
This exercise involves two converging lenses with focal lengths \( f_1 = 11.2 \, \text{cm} \) and \( f_2 = 20.0 \, \text{cm} \). A final image is formed at the position \( x = 31.3 \, \text{cm} \).

**Diagram Explanation:**
The diagram illustrates a system with two lenses and an object placed to the left of the first lens (designated as \( f_1 \)). 

- **Lens \( f_1 \):** Placed initially with an object positioned to its left at distance \( p \).
- **Final Image:** Formed after the light passes through both lenses.
- **Lens \( f_2 \):** Located at a distance \( x \) from the first lens.
- **Distances:**
  - \( p \): Distance from the object to the first lens.
  - \( x \): Distance between two lenses.
  - \( d \): Total distance from the first lens to the final image.

**Problems:**

(a) **How far (in cm) to the left of the first lens should the object be positioned?**
   - Calculate the correct position of the object using lens formulas and apply the given focal lengths.

(b) **What is the overall magnification of the system?**
   - Determine the system’s magnification by multiplying the magnifications from each lens interaction.

(c) **Is the final image upright or inverted?**
   - Choose between upright and inverted based on the calculated values and lens properties.
   - The correct answer provided is 'inverted'.

**Objective:**
Understand the behavior of light through converging lenses and apply lens equations to solve for object position, magnification, and image orientation.
Transcribed Image Text:**Title: Optical System Analysis with Converging Lenses** **Overview:** This exercise involves two converging lenses with focal lengths \( f_1 = 11.2 \, \text{cm} \) and \( f_2 = 20.0 \, \text{cm} \). A final image is formed at the position \( x = 31.3 \, \text{cm} \). **Diagram Explanation:** The diagram illustrates a system with two lenses and an object placed to the left of the first lens (designated as \( f_1 \)). - **Lens \( f_1 \):** Placed initially with an object positioned to its left at distance \( p \). - **Final Image:** Formed after the light passes through both lenses. - **Lens \( f_2 \):** Located at a distance \( x \) from the first lens. - **Distances:** - \( p \): Distance from the object to the first lens. - \( x \): Distance between two lenses. - \( d \): Total distance from the first lens to the final image. **Problems:** (a) **How far (in cm) to the left of the first lens should the object be positioned?** - Calculate the correct position of the object using lens formulas and apply the given focal lengths. (b) **What is the overall magnification of the system?** - Determine the system’s magnification by multiplying the magnifications from each lens interaction. (c) **Is the final image upright or inverted?** - Choose between upright and inverted based on the calculated values and lens properties. - The correct answer provided is 'inverted'. **Objective:** Understand the behavior of light through converging lenses and apply lens equations to solve for object position, magnification, and image orientation.
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