Ina microscope of the type shown in the figure, the focal length of the objective is 5.64 cm, and that of the eyepiece is 9.85 cm. The distance between the lenses is 26.7 cm. (a) What is the tube length s? (b) If image I in the figure is to be just inside focal point F'1, how far from the objective should the object be? What then are (c) the lateral magnification m of the objective, (d) the angular magnification mẹ of the eyepiece, and (e) the overall magnification M of the microscope? Eyepiece Objective Parallel rays To distant virtual image

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Chapter1: Units, Trigonometry. And Vectors
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In a microscope of the type shown in the figure, the focal length of the objective is 5.64 cm, and that of the eyepiece is 9.85 cm. The distance between the lenses is 26.7 cm. (a) What is the tube length \( s \)? (b) If image \( I \) in the figure is to be just inside focal point \( F'_1 \), how far from the objective should the object be? What then are (c) the lateral magnification \( m \) of the objective, (d) the angular magnification \( m_g \) of the eyepiece, and (e) the overall magnification \( M \) of the microscope?

### Diagram Explanation

The diagram depicts a microscope setup with the following components:

- **Objective Lens**: The focal lengths \( F_1 \) and \( F_2 \) of the objective lens are indicated, with light rays converging to form an image.
- **Eyepiece**: The eyepiece lens has focal points depicted as \( F'_1 \), with parallel rays emerging for distant viewing.
- **Distance Markers**: The distances \( d_o \), \( d_e \), and \( s \) (tube length) are labeled along the optical axis.
- **Virtual Image**: The setup shows the creation of a virtual image that is viewed by the eyepiece.

### Calculations and Answers

- **(a) Tube Length \( s \)**: \( 42.2 \, \text{cm} \)
- **(b) Object Distance from Objective**: \( -6.83 \, \text{cm} \)
- **(c) Lateral Magnification \( m \)**: \( -4.73 \) (unitless)
- **(d) Angular Magnification \( m_g \)**: \( 3.71 \) (unitless)
- **(e) Overall Magnification \( M \)**: \( -17.5 \) (unitless)

These calculations involve understanding the optical principles of magnification and image formation in a compound microscope.
Transcribed Image Text:In a microscope of the type shown in the figure, the focal length of the objective is 5.64 cm, and that of the eyepiece is 9.85 cm. The distance between the lenses is 26.7 cm. (a) What is the tube length \( s \)? (b) If image \( I \) in the figure is to be just inside focal point \( F'_1 \), how far from the objective should the object be? What then are (c) the lateral magnification \( m \) of the objective, (d) the angular magnification \( m_g \) of the eyepiece, and (e) the overall magnification \( M \) of the microscope? ### Diagram Explanation The diagram depicts a microscope setup with the following components: - **Objective Lens**: The focal lengths \( F_1 \) and \( F_2 \) of the objective lens are indicated, with light rays converging to form an image. - **Eyepiece**: The eyepiece lens has focal points depicted as \( F'_1 \), with parallel rays emerging for distant viewing. - **Distance Markers**: The distances \( d_o \), \( d_e \), and \( s \) (tube length) are labeled along the optical axis. - **Virtual Image**: The setup shows the creation of a virtual image that is viewed by the eyepiece. ### Calculations and Answers - **(a) Tube Length \( s \)**: \( 42.2 \, \text{cm} \) - **(b) Object Distance from Objective**: \( -6.83 \, \text{cm} \) - **(c) Lateral Magnification \( m \)**: \( -4.73 \) (unitless) - **(d) Angular Magnification \( m_g \)**: \( 3.71 \) (unitless) - **(e) Overall Magnification \( M \)**: \( -17.5 \) (unitless) These calculations involve understanding the optical principles of magnification and image formation in a compound microscope.
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