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 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 40c
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
For each thin lens shown in Fig. E34.37, calculate the location of the image of an object that is 18.0 cm to the left of the lens. The lens material has a refractive index of 1.50, and the radii of curvature shown are only the magnitudes.
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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
BIO The Lens of the Eye. The crystalline lens of the human eye is a double-convex lens made of material having an index of refraction of 1.44 (although this varies). Its focal length in air is about 8.0 mm, which also varies. We shall assume that the radii of curvature of its two surfaces have the same magnitude. Find the radii of curvature of this lens.
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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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