onverging and the diverging lens, respectively). An object is located at x = -1.80 cm to the left of the converging lens and the focal lengths of the convergir nd diverging lenses are 5.50 cm and -7.70 cm, respectively. HINT F. 0 Fp Fc x= 0 (a) Determine the x-location in cm of the final image. cm b) Determine its overall magnification.
onverging and the diverging lens, respectively). An object is located at x = -1.80 cm to the left of the converging lens and the focal lengths of the convergir nd diverging lenses are 5.50 cm and -7.70 cm, respectively. HINT F. 0 Fp Fc x= 0 (a) Determine the x-location in cm of the final image. cm b) Determine its overall magnification.
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![### Optical System Analysis
#### Problem Description:
A converging lens is placed at \( x = 0 \), a distance \( d = 9.00 \) cm to the left of a diverging lens as shown in the figure below (where \( F_C \) and \( F_D \) locate the focal points for the converging and the diverging lens, respectively).
- An object is located at \( x = -1.80 \) cm to the left of the converging lens.
- The focal lengths of the converging and diverging lenses are \( 5.50 \) cm and \( -7.70 \) cm, respectively.
#### Diagram Explanation:
- The diagram shows an optical system consisting of two lenses: a converging lens on the left and a diverging lens on the right.
- The position \( x = 0 \) marks the location of the converging lens.
- The distance between the lenses, denoted by \( d \), is given as \( 9.00 \) cm.
- The focal points of the converging lens (\( F_C \)) are shown on both sides of the lens and aligned with the principal axis.
- Similarly, the focal points of the diverging lens (\( F_D \)) are indicated on both sides, aligned with the principal axis.
- An object is positioned to the left of the converging lens at \( x = -1.80 \) cm.
#### Questions:
(a) Determine the \( x \)-location in cm of the final image.
\[ \boxed{\ \text{cm} \} \]
(b) Determine its overall magnification.
\[ \boxed{\ \} \]
#### Hint:
Make use of the lens equations and principles of optics to solve for the required parameters.
Feel free to utilize the provided graph and focal length information to accurately determine the position and magnification of the final image produced by the given optical system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a604148-c777-4cb2-a23a-e827df875cbf%2Ffbbe4e81-b4b2-4652-8515-d2c73c1ca5aa%2Fqhspvdi_processed.png&w=3840&q=75)
Transcribed Image Text:### Optical System Analysis
#### Problem Description:
A converging lens is placed at \( x = 0 \), a distance \( d = 9.00 \) cm to the left of a diverging lens as shown in the figure below (where \( F_C \) and \( F_D \) locate the focal points for the converging and the diverging lens, respectively).
- An object is located at \( x = -1.80 \) cm to the left of the converging lens.
- The focal lengths of the converging and diverging lenses are \( 5.50 \) cm and \( -7.70 \) cm, respectively.
#### Diagram Explanation:
- The diagram shows an optical system consisting of two lenses: a converging lens on the left and a diverging lens on the right.
- The position \( x = 0 \) marks the location of the converging lens.
- The distance between the lenses, denoted by \( d \), is given as \( 9.00 \) cm.
- The focal points of the converging lens (\( F_C \)) are shown on both sides of the lens and aligned with the principal axis.
- Similarly, the focal points of the diverging lens (\( F_D \)) are indicated on both sides, aligned with the principal axis.
- An object is positioned to the left of the converging lens at \( x = -1.80 \) cm.
#### Questions:
(a) Determine the \( x \)-location in cm of the final image.
\[ \boxed{\ \text{cm} \} \]
(b) Determine its overall magnification.
\[ \boxed{\ \} \]
#### Hint:
Make use of the lens equations and principles of optics to solve for the required parameters.
Feel free to utilize the provided graph and focal length information to accurately determine the position and magnification of the final image produced by the given optical system.
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