Textbook Question
Repeat Exercise 34.41 using the same lenses except for the following changes: The second lens is a diverging lens having a focal length of magnitude 60.0 cm.
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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 42c
An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. Draw a principal-ray diagram.
Verified step by step guidance1
Understand the problem: The object is placed 16.0 cm to the left of the lens, and the image is formed 36.0 cm to the right of the lens. This indicates that the lens is converging (convex) since it forms a real image on the opposite side. We will draw a principal-ray diagram to represent this setup.
Step 1: Draw the optical axis as a horizontal line. Mark the position of the lens at the center of the diagram with a vertical line. Label the focal points (F) on both sides of the lens. The focal length can be calculated using the lens formula, but for the diagram, we will approximate the focal points based on the given distances.
Step 2: Place the object 16.0 cm to the left of the lens. Represent the object as an upright arrow perpendicular to the optical axis. Label the object as 'O'.
Step 3: Draw the principal rays: (a) The first ray travels parallel to the optical axis from the top of the object and refracts through the lens, passing through the focal point on the opposite side. (b) The second ray passes through the center of the lens without bending. (c) The third ray passes through the focal point on the object's side, refracts through the lens, and travels parallel to the optical axis.
Step 4: Extend the refracted rays on the right side of the lens. The point where these rays converge represents the position of the image. Draw the image as an arrow at this location, inverted relative to the object. Label the image as 'I'.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Lens Types
Lenses can be classified into two main types: converging (convex) and diverging (concave). Converging lenses focus parallel rays of light to a point, while diverging lenses spread out light rays. Understanding the type of lens is crucial for predicting how it will manipulate light and form images.
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07:58
Thin Lens Equation
Ray Diagrams
Ray diagrams are graphical representations used to illustrate how light rays interact with lenses. They typically include principal rays such as the parallel ray, the focal ray, and the central ray, which help determine the location and characteristics of the image formed by the lens. Drawing these diagrams is essential for visualizing the behavior of light.
Recommended video:
06:37Ray Diagrams for Converging Lenses
Image Formation
Image formation by lenses involves the relationship between the object distance, image distance, and focal length, described by the lens formula (1/f = 1/do + 1/di). The nature of the image (real or virtual, upright or inverted) depends on the object's position relative to the lens's focal point. Understanding this relationship is key to solving problems related to lenses.
Recommended video:
05:51Refraction at Spherical Surfaces
Related Practice
Textbook Question
A lensmaker wants to make a magnifying glass from glass that has an index of refraction n = 1.55 and a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?
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Textbook Question
A 1.20 cm tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm.
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Textbook Question
An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. If the object is 8.00 mm tall, how tall is the image? Is it erect or inverted?
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Textbook Question
A converging lens with a focal length of 9.00 cm forms an image of a 4.00 mm tall real object that is to the left of the lens. The image is 1.30 cm tall and erect. Where are the object and image located? Is the image real or virtual?
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Textbook Question
You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. If the dimensions of the picture on a 35 mm color slide are 24 mm ✖ 36 mm, what is the minimum size of the projector screen required to accommodate the image?
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