Textbook Question
BIO A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. Is she nearsighted or farsighted?
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Ch 34: Geometric Optics
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 33, Problem 58a
A thin lens with a focal length of 6.00 cm is used as a simple magnifier. What angular magnification is obtainable with the lens if the object is at the focal point?
Verified step by step guidance1
Understand the concept of angular magnification: Angular magnification (M) for a simple magnifier is defined as the ratio of the angular size of the image to the angular size of the object when viewed with the naked eye at the near point. For a lens, when the object is placed at the focal point, the angular magnification is given by the formula: , where is the near point distance (typically 25 cm for a normal human eye) and is the focal length of the lens.
Substitute the given values into the formula: The focal length of the lens is cm, and the near point distance is cm. Substitute these values into the formula: .
Simplify the fraction: Calculate the value of the fraction to determine the contribution of the lens's focal length to the magnification.
Add 1 to the result of the fraction: After simplifying the fraction, add 1 to account for the additional magnification provided by the lens when the object is at the focal point.
Interpret the result: The final value represents the angular magnification obtainable with the lens when the object is placed at the focal point. This value indicates how much larger the object appears when viewed through the magnifier compared to the naked eye.
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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. In this case, a focal length of 6.00 cm indicates that light rays entering the lens parallel to its axis will converge at a point 6.00 cm away from the lens. This property is crucial for understanding how lenses form images and magnify objects.
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Angular Magnification
Angular magnification is a measure of how much larger an object appears when viewed through a lens compared to the naked eye. It is defined as the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the same eye without the lens. For a simple magnifier, this concept helps quantify the lens's effectiveness in enlarging the apparent size of an object.
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Simple Magnifier
A simple magnifier is a type of lens, typically a convex lens, used to produce a magnified image of an object. When the object is placed at or near the focal point of the lens, the lens creates a virtual image that appears larger than the object itself. Understanding how a simple magnifier works is essential for calculating the angular magnification and appreciating its practical applications in various fields.
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Related Practice
Textbook Question
The focal length of a simple magnifier is 8.00 cm. Assume the magnifier is a thin lens placed very close to the eye. If the object is 1.00 mm high, what is the height of its image formed by the magnifier?
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Textbook Question
A telescope is constructed from two lenses with focal lengths of 95.0 cm and 15.0 cm, the 95.0 cm lens being used as the objective. Both the object being viewed and the final image are at infinity. Find the height of the image formed by the objective of a building 60.0 m tall, 3.00 km away.
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Textbook Question
BIO A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. What focal length contact lens is needed, and what is its power in diopters?
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Textbook Question
BIO Ordinary Glasses. Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their power in diopters?
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