Domanda del libro di testo
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?
2016
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Ch 34: Geometric Optics
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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TOC.tableOfContents
- 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
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Capitolo 33, Problema 59b
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?
Guida verificata passo dopo passo1
Identify the given values: The focal length of the lens \( f = 8.00 \; \text{cm} \) and the object height \( h_o = 1.00 \; \text{mm} \). The goal is to find the height of the image \( h_i \).
Use the lens formula to find the image distance \( v \): \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \), where \( f \) is the focal length, \( u \) is the object distance, and \( v \) is the image distance. Rearrange to solve for \( v \): \( \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \).
Determine the magnification \( M \) of the lens using the formula \( M = \frac{h_i}{h_o} = \frac{v}{u} \). Rearrange to solve for \( h_i \): \( h_i = M \cdot h_o \).
Substitute the values of \( v \), \( u \), and \( h_o \) into the magnification formula to calculate the image height \( h_i \). Ensure that all units are consistent (e.g., convert \( h_o \) to cm if necessary).
Interpret the result: The sign of \( h_i \) will indicate whether the image is upright or inverted, and the magnitude will give the size of the image formed by the magnifier.
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Focal Length
The focal length of a lens is the distance from the lens to the focal point, where parallel rays of light converge. For a simple magnifier, a positive focal length indicates that it is a converging lens. The focal length is crucial for determining how the lens will magnify an object and affects the size of the image formed.
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Magnification
Magnification is the ratio of the height of the image to the height of the object. It can be calculated using the formula: magnification (M) = image height (h') / object height (h). In the case of a magnifier, the magnification also depends on the focal length and the distance of the object from the lens, allowing us to determine how much larger the image appears compared to the actual object.
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Thin Lens Formula
The thin lens formula relates the object distance (d_o), image distance (d_i), and focal length (f) of a lens: 1/f = 1/d_o + 1/d_i. This formula is essential for understanding how lenses form images and can be used to find the image distance when the object distance and focal length are known. It helps in calculating the position and size of the image produced by the magnifier.
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