Compound Microscope: Solving for Objective Focal Length

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SUMMARY

The discussion focuses on calculating the focal length of the objective lens in a compound microscope with a total tube length of 18.0 cm, an eyepiece focal length of 2.08 cm, and a magnification of -4350. The user attempted to apply the formulas for image distance and magnification but struggled with isolating the objective focal length (fo). The correct approach involves recognizing that the total length of the microscope tube (18.0 cm) is equal to the sum of the image distance (di) and the objective focal length (fo), leading to the equation fo = (dN)/(Mfe + N) for accurate calculations.

PREREQUISITES
  • Understanding of optical physics, specifically lens equations.
  • Familiarity with the concepts of magnification in optical systems.
  • Knowledge of algebraic manipulation for solving equations.
  • Basic principles of compound microscope design and function.
NEXT STEPS
  • Review the lens maker's equation for calculating focal lengths in optical systems.
  • Study the principles of magnification and how it relates to image distance and object distance.
  • Explore practical examples of compound microscope calculations using different focal lengths.
  • Learn about the significance of relaxed eye viewing in optical instruments.
USEFUL FOR

This discussion is beneficial for physics students, optical engineers, and anyone involved in designing or using optical instruments, particularly in understanding the calculations related to compound microscopes.

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A compound microscope has the objective and eyepiece mounted in a tube that is 18.0 cm long. The focal length of the eyepiece is 2.08 cm, and the near-point distance of the person using the microscope is 25.0 cm. If the person can view the image produced by the microscope with a completely relaxed eye, and the magnification is -4350, what is the focal length of the objective? (Include the sign.)

I tried using the equations

d i =d- fo

M = (d i * N)/(fo*fe)

since I could not find d i b/c I didn't know fo, I substituted d-fo for d i in the second equation. When I isolated fo, I got

fo=(dN)/(Mfe +N)

I thought that I was doing this right...what did I mess up?
 
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did I do an algebraic mistake or...I assumed that the 18 cm = d...was that a wrong assumption to make?
 

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