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Ch 34: Ray Optics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 34: Ray OpticsProblem 40
Chapter 34, Problem 40

An object is 12 cm in front of a concave mirror with a focal length of 20 cm. Use ray tracing to locate the image. Is the image upright or inverted?

Verified step by step guidance
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Start by understanding the problem: A concave mirror has a focal length of 20 cm, and the object is placed 12 cm in front of it. We need to use ray tracing to locate the image and determine its orientation (upright or inverted).
Draw a diagram of the concave mirror. Mark the principal axis, the focal point (F) at 20 cm from the mirror, and the center of curvature (C) at 40 cm from the mirror. Place the object 12 cm in front of the mirror on the principal axis.
Trace the first ray: Draw a ray from the top of the object parallel to the principal axis. After reflecting off the mirror, this ray will pass through the focal point (F).
Trace the second ray: Draw a ray from the top of the object passing through the focal point (F) toward the mirror. After reflecting, this ray will travel parallel to the principal axis.
Locate the image: The point where the two reflected rays intersect is the location of the image. Since the object is within the focal length of the mirror, the image will form on the same side as the object, be virtual, upright, and magnified.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Concave Mirror

A concave mirror is a spherical mirror that curves inward, resembling a portion of a sphere. It has the ability to converge light rays that are parallel to its principal axis, focusing them at a point known as the focal point. The distance from the mirror's surface to this focal point is called the focal length, which is positive for concave mirrors.
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Ray Diagrams for Concave Mirrors

Ray Tracing

Ray tracing is a graphical method used to determine the position and characteristics of an image formed by a mirror or lens. In this technique, at least two principal rays are drawn from the object: one parallel to the principal axis that reflects through the focal point, and another passing through the focal point that reflects parallel to the principal axis. The intersection of these rays indicates the location of the image.
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Ray Diagrams for Diverging Lenses

Image Characteristics

The characteristics of an image formed by a mirror include its orientation (upright or inverted), size (larger or smaller), and type (real or virtual). For concave mirrors, if the object is located between the focal point and the mirror, the image will be virtual and upright. If the object is beyond the focal point, the image will be real and inverted, with its size depending on the object's distance from the mirror.
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Mirror Equation
Related Practice
Textbook Question

A 1.0-cm-tall object is 60 cm in front of a diverging lens that has a −30 cm focal length. Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.

Textbook Question

A 2.0-cm-tall object is 15 cm in front of a plano-convex polystyrene plastic lens that has a 13 cm radius of curvature. What are the (a) position and (b) height of the image?

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Textbook Question

An advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers. To acquire data from memory, the central processing unit sends a light-pulse request to the memory unit. The memory unit processes the request, then sends a data pulse back to the central processing unit. The memory unit takes 0.5 ns to process a request. If the information has to be obtained from memory in 2.0 ns, what is the maximum distance the memory unit can be from the central processing unit?

Textbook Question

A laser beam in air is incident on a liquid at an angle of 53° with respect to the normal. The laser beam's angle in the liquid is 35°. What is the liquid's index of refraction?

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Textbook Question

The place you get your hair cut has two nearly parallel mirrors 5.0 m apart. As you sit in the chair, your head is 2.0 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be? Neglect the thickness of your head.

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Textbook Question

A red ball is placed at point A in FIGURE P34.44. What are the (x, y) coordinates of each image?

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