Textbook Question
Find the focal length of the glass lens in FIGURE EX34.28.
Ch 34: Ray Optics
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 34, Problem 25
Find the focal length of the plano-concave polystyrene plastic lens in FIGURE EX34.25.
Verified step by step guidance1
Step 1: Understand the lens type and its geometry. A plano-concave lens has one flat surface and one inwardly curved surface. The focal length of such a lens can be calculated using the lens maker's formula.
Step 2: Write the lens maker's formula: \( \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \), where \( f \) is the focal length, \( n \) is the refractive index of the lens material, \( R_1 \) is the radius of curvature of the first surface, and \( R_2 \) is the radius of curvature of the second surface.
Step 3: Identify the values from the problem. For a plano-concave lens, \( R_1 \) (flat surface) is infinite, so \( \frac{1}{R_1} = 0 \). \( R_2 \) is the radius of curvature of the concave surface, which is given as 40 cm. The refractive index of polystyrene plastic is approximately \( n = 1.59 \).
Step 4: Substitute the values into the lens maker's formula: \( \frac{1}{f} = (1.59 - 1) \left( 0 - \frac{1}{-40} \right) \). Note that the negative sign for \( R_2 \) is due to the concave surface.
Step 5: Simplify the equation to find \( f \). Rearrange the formula to solve for \( f \), ensuring proper handling of the negative sign and refractive index. This will yield the focal length of the plano-concave lens.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Focal Length
The focal length of a lens is the distance from the lens to the focal point, where parallel rays of light converge or appear to diverge. For a plano-concave lens, which is a diverging lens, the focal length is negative, indicating that the focal point is virtual and located on the same side as the incoming light.
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Lens Maker's Equation
The Lens Maker's Equation relates the focal length of a lens to the radii of curvature of its surfaces and the refractive index of the material. It is given by the formula: 1/f = (n - 1) * (1/R1 - 1/R2), where f is the focal length, n is the refractive index, and R1 and R2 are the radii of curvature of the lens surfaces. This equation is essential for calculating the focal length of lenses with different shapes.
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Plano-Concave Lens
A plano-concave lens has one flat (plano) surface and one inwardly curved (concave) surface. This type of lens diverges light rays that are incident on it, causing them to spread out. The curvature of the concave surface determines the lens's focal length, which is crucial for applications in optics where light manipulation is required.
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Related Practice
Textbook Question
An object is 20 cm in front of a converging lens with a focal length of 10 cm. Use ray tracing to determine the location of the image. Is the upright or inverted?
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Textbook Question
A goldfish lives in a 50-cm-diameter spherical fish bowl. The fish sees a cat watching it. If the cat's face is 20 cm from the edge of the bowl, how far from the edge does the fish see it as being? (You can ignore the thin glass wall of the bowl.)
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Textbook Question
A giant ocean tank at an aquarium has acrylic plastic walls 18 cm thick. The index of refraction of acrylic plastic is 1.49. A fish is 220 cm from the inside wall. To a viewer on the outside, how far does the fish appear to be from the outside wall? Hint: The of the first refraction is the object for the second refraction.
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Textbook Question
To a fish in an aquarium, the 4.00-mm-thick walls appear to be only 3.50 mm thick. What is the index of refraction of the walls?
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Textbook Question
A 1.0-cm-tall candle flame is 60 cm from a lens with a focal length of 20 cm. What are the distance and the height of the flame's image?
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