Chapter 34: Problem 59
The focal length of the eyepiece of a certain microscope is 18.0 mm. The focal length of the objective is 8.00 mm. The distance between objective and eyepiece is 19.7 cm. The final image formed by the eyepiece is at infinity. Treat all lenses as thin. (a) What is the distance from the objective to the object being viewed? (b) What is the magnitude of the linear magnification produced by the objective? (c) What is the overall angular magnification of the microscope?
Short Answer
Step by step solution
Understand the Problem
Relation for Lens Equation
Find the Image Distance for Objective
Solve for Objective Object Distance
Linear Magnification of the Objective
Overall Angular Magnification
Final Calculations
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Focal Length
- A shorter focal length means the lens is more powerful and converges light quickly.
- A longer focal length indicates a weaker lens that takes longer to bring light to a focus.
The objective with a shorter focal length is capable of creating a highly magnified intermediate image, which the eyepiece further magnifies for the viewer.
Lens Formula
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]where:
- \( f \) is the focal length of the lens.
- \( d_o \) is the distance from the object to the lens.
- \( d_i \) is the distance from the lens to the image.
Magnification
Linear magnification for a lens, like the objective in a microscope, is given by:
- \( m = -\frac{d_i}{d_o} \)
The total magnification of the microscope combines the eyepiece's angular magnification with the objective's linear magnification, providing the viewer with a greatly enhanced view of the object.
Thin Lens Equation
By treating lenses as thin, their focal lengths can be effectively modeled with the lens formula. Thin lens assumptions simplify complex systems, like microscopes, into manageable data points. This aids in calculating crucial measures, like object and image distances, and magnifications.
Within the provided exercise, assuming thin lenses helps find key distances and magnifications with minimal computational effort, using the relations derived from the lens formula.
While this model is quite effective for most calculations, it's important to remember that real lenses may have limited thickness, affecting precision in professional applications.