A Two-Lens System < 19 of 22 (> Constants Part A A compound lens system consists of two converging lenses, one at z= -20.0 cm with focal length fi = +10.0 cm, and the other at z= +20.0 cm with focal length fa- +8.00 cm. Eigure 1An object 1.00 centimeter tall is placed at z= -50.0 cm. What is the location of the final image produced by the compound lens system? Give the x coordinate of the image. Express your answer in centimeters, to three significant figures or as a fraction. > View Available Hint(s) z= 15 cm Submit Previous Answrs X Incorrect; Try Again; 4 attempts remaining Part B Complete previous part(s) Part C Complete previous part(s) Now remove the two lenses at z - +20.0 cm and z--20.0 cm and replace them with a single lens of focal length fz at z -0. We want to choose this new lens so that it produces an image at the same location as before. • Part D Figure < 1 of 1 What is the focal length of the new lens at the origin? Express your answer in centimeters, to three significant figures or as a fraction. > View Available Hint(s) cm Submit

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**Homework 5: Geometric Optics**

**A Two-Lens System**

A compound lens system consists of two converging lenses, one at \( z = -20.0 \, \text{cm} \) with focal length \( f_1 = +10.0 \, \text{cm} \), and the other at \( z = +20.0 \, \text{cm} \) with focal length \( f_2 = +8.00 \, \text{cm} \). (Figure 1) An object 1.00 centimeter tall is placed at \( z = -50.0 \, \text{cm} \).

**Part A**

What is the location of the final image produced by the compound lens system? Give the \( x \) coordinate of the image.

Express your answer in centimeters, to three significant figures or as a fraction.

- **Answer Input Box**: \( z = \text{15} \, \text{cm} \)

- **Feedback**: Incorrect; Try Again; 4 attempts remaining

**Part B** and **Part C** (incomplete; need to complete previous parts to proceed)

Now remove the two lenses at \( z = +20.0 \, \text{cm} \) and \( z = -20.0 \, \text{cm} \) and replace them with a single lens of focal length \( f_3 \) at \( z = 0 \). We want to choose this new lens so that it produces an image at the same location as before.

**Part D**

What is the focal length of the new lens at the origin?

Express your answer in centimeters, to three significant figures or as a fraction.

- **Answer Input Box**: \( f_3 = \, \text{cm} \)

**Figure Description**

The figure shows two lenses, \( f_1 \) and \( f_2 \), along a horizontal optical axis with an object represented by an upwards green arrow on the left side of the lens system. The lenses are arranged with \( f_1 \) at a negative position and \( f_2 \) at a positive position, as described in the system problem above.

**Constants**: Specific constants were not provided but are typically available via a constants section on the educational platform to aid calculations.
Transcribed Image Text:**Homework 5: Geometric Optics** **A Two-Lens System** A compound lens system consists of two converging lenses, one at \( z = -20.0 \, \text{cm} \) with focal length \( f_1 = +10.0 \, \text{cm} \), and the other at \( z = +20.0 \, \text{cm} \) with focal length \( f_2 = +8.00 \, \text{cm} \). (Figure 1) An object 1.00 centimeter tall is placed at \( z = -50.0 \, \text{cm} \). **Part A** What is the location of the final image produced by the compound lens system? Give the \( x \) coordinate of the image. Express your answer in centimeters, to three significant figures or as a fraction. - **Answer Input Box**: \( z = \text{15} \, \text{cm} \) - **Feedback**: Incorrect; Try Again; 4 attempts remaining **Part B** and **Part C** (incomplete; need to complete previous parts to proceed) Now remove the two lenses at \( z = +20.0 \, \text{cm} \) and \( z = -20.0 \, \text{cm} \) and replace them with a single lens of focal length \( f_3 \) at \( z = 0 \). We want to choose this new lens so that it produces an image at the same location as before. **Part D** What is the focal length of the new lens at the origin? Express your answer in centimeters, to three significant figures or as a fraction. - **Answer Input Box**: \( f_3 = \, \text{cm} \) **Figure Description** The figure shows two lenses, \( f_1 \) and \( f_2 \), along a horizontal optical axis with an object represented by an upwards green arrow on the left side of the lens system. The lenses are arranged with \( f_1 \) at a negative position and \( f_2 \) at a positive position, as described in the system problem above. **Constants**: Specific constants were not provided but are typically available via a constants section on the educational platform to aid calculations.
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