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 lin 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? Eyеpiece Objective F2 Parallel rays To distant virtual image

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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? 
(c) What then are 
- (c) the lateral magnification \( m \) of the objective, 
- (d) the angular magnification \( m_g \) of the eyepiece, 
- (e) the overall magnification \( M \) of the microscope?

### Diagram Description:
The diagram is a ray diagram for a compound microscope consisting of an objective and an eyepiece. 

- The objective lens is marked with two focal points: \( F_1 \) and \( F_2 \). 
- The object \( O \) is placed before the objective lens.
- The light rays from the object converge at an image \( I' \) before diverging to pass through the eyepiece lens.
- The eyepiece lens has a focal point \( F_1' \) beyond which the rays emerge as parallel rays, indicating a virtual image formation.
- The tube length \( s \) is shown by a line indicating the distance from the back of the objective lens to the front of the eyepiece lens.
- The path of light through the microscope is indicated with red lines and arrows, showing the direction of light travel.

### Inputs for Calculation:
- (a) Number: [Input box] Units [Dropdown]
- (b) Number: [Input box] Units [Dropdown]
- (c) Number: [Input box] Units [Dropdown]
- (d) Number: [Input box] Units [Dropdown]
- (e) Number: [Input box] Units [Dropdown]
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? (c) What then are - (c) the lateral magnification \( m \) of the objective, - (d) the angular magnification \( m_g \) of the eyepiece, - (e) the overall magnification \( M \) of the microscope? ### Diagram Description: The diagram is a ray diagram for a compound microscope consisting of an objective and an eyepiece. - The objective lens is marked with two focal points: \( F_1 \) and \( F_2 \). - The object \( O \) is placed before the objective lens. - The light rays from the object converge at an image \( I' \) before diverging to pass through the eyepiece lens. - The eyepiece lens has a focal point \( F_1' \) beyond which the rays emerge as parallel rays, indicating a virtual image formation. - The tube length \( s \) is shown by a line indicating the distance from the back of the objective lens to the front of the eyepiece lens. - The path of light through the microscope is indicated with red lines and arrows, showing the direction of light travel. ### Inputs for Calculation: - (a) Number: [Input box] Units [Dropdown] - (b) Number: [Input box] Units [Dropdown] - (c) Number: [Input box] Units [Dropdown] - (d) Number: [Input box] Units [Dropdown] - (e) Number: [Input box] Units [Dropdown]
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