Textbook Question
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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Table of contents
- 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: 9780137344796Not the one you use?Change textbook
Chapter 35, Problem 13
What is the f-number of a relaxed eye with the pupil fully dilated to 8.0 mm? Model the eye as a single lens 2.4 cm in front of the retina.
Verified step by step guidance1
Step 1: Understand the concept of the f-number. The f-number (or focal ratio) is defined as the ratio of the focal length of a lens to the diameter of its aperture. Mathematically, it is expressed as: , where is the focal length and is the aperture diameter.
Step 2: Identify the given values in the problem. The diameter of the pupil (aperture) is given as , which can be converted to centimeters: . The distance from the lens to the retina is given as , which represents the focal length of the eye.
Step 3: Substitute the values into the f-number formula. Using and , the formula becomes: .
Step 4: Simplify the fraction to determine the f-number. Divide the focal length by the aperture diameter to find the ratio.
Step 5: Interpret the result. The f-number represents how much light the eye can gather when the pupil is fully dilated. A smaller f-number indicates a larger aperture and more light-gathering ability.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
F-number (focal ratio)
The f-number, or focal ratio, is a dimensionless number that describes the aperture size of a lens relative to its focal length. It is calculated by dividing the focal length of the lens by the diameter of the entrance pupil. A lower f-number indicates a larger aperture, allowing more light to enter, which is crucial for understanding how the eye focuses light onto the retina.
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Pupil diameter
The pupil diameter refers to the size of the opening in the iris that allows light to enter the eye. In this context, a fully dilated pupil of 8.0 mm serves as the entrance pupil for calculating the f-number. The size of the pupil can significantly affect the amount of light that reaches the retina and influences the eye's ability to focus in different lighting conditions.
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Lens model of the eye
Modeling the eye as a single lens simplifies the complex optical system of the eye into a basic lens formula. In this model, the distance from the lens to the retina (2.4 cm) represents the effective focal length. This approach allows for the application of lens equations to determine how the eye focuses light, which is essential for calculating the f-number in this scenario.
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Related Practice
Textbook Question
A camera’s close-up lens is aimed at a butterfly 200 mm in front of the lens, creating a focused on the detector 50 mm behind the lens. A proper exposure requires an f-number of F8.0. What is the correct diameter of the lens aperture?
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Textbook Question
Ramon has contact lenses with the prescription +2.0 D. What eye condition does Ramon have?
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Textbook Question
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?
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Textbook Question
A magnifier has a magnification of 5x. How far from the lens should an object be held so that its is seen at the near-point distance of 25 cm? Assume that your eye is immediately behind the lens.
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Textbook Question
A camera takes a properly exposed photo at F5.6 and 1/125 s. What shutter speed should be used if the lens is changed to F4.0?
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