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Three-lens systems. In the figure, stick figure O (the object) stands on the common central axis of three thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closest to O, which is at object distance p1. Lens 2 is mounted within the middle boxed region, at distance d2 from lens 1. Lens 3 is mounted in the farther boxed region, at distance d23 from lens 2. (see the table below, all distances are given in centimeters). The type of lens is indicated by C for converging and D for diverging; the number after C or D is the distance between a lens and either of the focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance /3 for the (final) image produced by lens 3 (the final image produced by the system) and (b) the overall lateral magnification M for the system, including signs. Also, determine whether the final Image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of lens 3 as object O or on the opposite side.

Three-lens systems. In the figure, stick figure O (the object) stands on the common central axis of three thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closest to O, which is at object distance p1. Lens 2 is mounted within the middle boxed region, at distance d2 from lens 1. Lens 3 is mounted in the farther boxed region, at distance d23 from lens 2. (see the table below, all distances are given in centimeters). The type of lens is indicated by C for converging and D for diverging; the number after C or D is the distance between a lens and either of the focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance /3 for the (final) image produced by lens 3 (the final image produced by the system) and (b) the overall lateral magnification M for the system, including signs. Also, determine whether the final Image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of lens 3 as object O or on the opposite side.

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### Chapter 34, Problem 098: Three-Lens Systems #### Problem Statement: In the figure, stick figure O (the object) stands on the common central axis of three thin, symmetric lenses, which are mounted in the boxed regions. 1. **Lens 1** is mounted within the boxed region closest to O, which is at object distance \( p_1 \). 2. **Lens 2** is mounted within the middle boxed region, at distance \( d_{12} \) from lens 1. 3. **Lens 3** is mounted in the farther boxed region, at distance \( d_{23} \) from lens 2. The distances are given in centimeters. The type of lens is indicated by C for converging and D for diverging; the number after C or D is the focal length. The image distance for each lens is measured and analyzed to solve the following: Find: - (a) The image distance \( l_3 \) for the final image produced. - (b) The overall lateral magnification \( M \) for the system, including signs. - (c) Determine whether the final image is real (R) or virtual (V). - (d) Inverted (I) or noninverted (NI) from object O. - (e) Whether the final image is on the same side of lens 3 as object O or on the opposite side. ##### Provided Data: - \( p_1 \): +1.1 - Lens 1: \( C, 2.1 \) - \( d_{12} \): 12 cm - Lens 2: \( C, 3.6 \) - \( d_{23} \): 10 cm - Lens 3: \( C, 2.7 \) ##### Required: Input the correct values: (a) Number \( l_3 \): (b) Number \( M \): (c) Real or Virtual (R/V): (d) Inverted or Noninverted (I/NI): (e) Image side (same as object O or opposite): #### Accompanying Diagram Explanation: In the diagram provided, stick figure O (object) is positioned on the common axis of three lenses: - **Lens 1** (C, focal length 2.1 cm) - **Lens 2** (C, focal length 3.6 cm) positioned 12 cm from
Transcribed Image Text:### Chapter 34, Problem 098: Three-Lens Systems #### Problem Statement: In the figure, stick figure O (the object) stands on the common central axis of three thin, symmetric lenses, which are mounted in the boxed regions. 1. **Lens 1** is mounted within the boxed region closest to O, which is at object distance \( p_1 \). 2. **Lens 2** is mounted within the middle boxed region, at distance \( d_{12} \) from lens 1. 3. **Lens 3** is mounted in the farther boxed region, at distance \( d_{23} \) from lens 2. The distances are given in centimeters. The type of lens is indicated by C for converging and D for diverging; the number after C or D is the focal length. The image distance for each lens is measured and analyzed to solve the following: Find: - (a) The image distance \( l_3 \) for the final image produced. - (b) The overall lateral magnification \( M \) for the system, including signs. - (c) Determine whether the final image is real (R) or virtual (V). - (d) Inverted (I) or noninverted (NI) from object O. - (e) Whether the final image is on the same side of lens 3 as object O or on the opposite side. ##### Provided Data: - \( p_1 \): +1.1 - Lens 1: \( C, 2.1 \) - \( d_{12} \): 12 cm - Lens 2: \( C, 3.6 \) - \( d_{23} \): 10 cm - Lens 3: \( C, 2.7 \) ##### Required: Input the correct values: (a) Number \( l_3 \): (b) Number \( M \): (c) Real or Virtual (R/V): (d) Inverted or Noninverted (I/NI): (e) Image side (same as object O or opposite): #### Accompanying Diagram Explanation: In the diagram provided, stick figure O (object) is positioned on the common axis of three lenses: - **Lens 1** (C, focal length 2.1 cm) - **Lens 2** (C, focal length 3.6 cm) positioned 12 cm from
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