Domanda del libro di testo
A 20x telescope has a 12-cm-diameter objective lens. What minimum diameter must the eyepiece lens have to collect all the light rays from an on-axis distant source?
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Ch 35: Optical Instruments
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 35, Problema 16
A microscope has a 160 mm tube length. What focal-length objective will give total magnification ≈ 500x when used with an eyepiece having a focal length of 5.0 cm?
Guida verificata passo dopo passo1
Step 1: Understand the relationship between total magnification, the magnification of the objective lens, and the magnification of the eyepiece. Total magnification is the product of the magnification of the objective lens and the magnification of the eyepiece: \( M_{total} = M_{objective} \times M_{eyepiece} \).
Step 2: Calculate the magnification of the eyepiece using its focal length. The magnification of the eyepiece is given by \( M_{eyepiece} = \frac{25 \text{ cm}}{f_{eyepiece}} \), where 25 cm is the near point of the human eye. Substitute \( f_{eyepiece} = 5.0 \text{ cm} \) into the formula.
Step 3: Rearrange the total magnification formula to solve for the magnification of the objective lens: \( M_{objective} = \frac{M_{total}}{M_{eyepiece}} \). Substitute \( M_{total} = 500 \) and the value of \( M_{eyepiece} \) calculated in Step 2.
Step 4: Use the formula for the magnification of the objective lens: \( M_{objective} = \frac{L}{f_{objective}} \), where \( L \) is the tube length (160 mm or 16.0 cm) and \( f_{objective} \) is the focal length of the objective lens. Rearrange this formula to solve for \( f_{objective} \): \( f_{objective} = \frac{L}{M_{objective}} \).
Step 5: Substitute \( L = 16.0 \text{ cm} \) and the value of \( M_{objective} \) from Step 3 into the formula for \( f_{objective} \). This will give the focal length of the objective lens required to achieve the desired total magnification.
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Total Magnification
Total magnification in a microscope is the product of the magnification of the objective lens and the eyepiece. It indicates how much larger an object appears compared to its actual size. For example, if the objective lens has a magnification of 40x and the eyepiece has a magnification of 10x, the total magnification would be 400x. Understanding this relationship is crucial for determining the required specifications of the lenses.
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Total Internal Reflection
Focal Length
Focal length is the distance from the lens to the point where parallel rays of light converge to a single point. In microscopes, the focal length of the objective lens affects the magnification and the working distance. A shorter focal length typically results in higher magnification, which is essential for observing small details in specimens. Knowing how to calculate and apply focal lengths is vital for achieving the desired total magnification.
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Lens Formula
The lens formula relates the object distance, image distance, and focal length of a lens. It is expressed as 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. This formula is fundamental in optics for determining how lenses will behave in a system, especially in microscopes where precise calculations are necessary to achieve specific magnifications.
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