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 Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 34, Problem 56a
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 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. What is the magnitude of the linear magnification produced by the objective?
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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
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
Resolution of a Microscope. The image formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. What is the angular magnification of the microscope?
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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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