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Ch. 32 - Light: Reflection and Refraction
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 32 - Light: Reflection and RefractionProblem 68cd
Chapter 31, Problem 68cd

(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 32–2 on plane mirrors?

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1
To determine the magnification of a plane mirror, recall the formula for magnification: M = - rac{q}{p}, where q is the image distance and p is the object distance. For a plane mirror, the image distance q is equal in magnitude to the object distance p, but with opposite sign.
Substitute q = -p into the magnification formula. This simplifies to M = - rac{-p}{p} = 1. Thus, the magnification of a plane mirror is always 1, meaning the image is the same size as the object.
For part (d), refer to Section 32–2, which discusses the properties of plane mirrors. Plane mirrors produce virtual images that are upright, laterally inverted, and the same size as the object. This is consistent with the magnification result of M = 1 derived in part (c).
Additionally, the discussion in Section 32–2 emphasizes that the image distance q is equal in magnitude to the object distance p, which aligns with the derivation of the magnification formula for a plane mirror.
In conclusion, the results in parts (b) and (c) are fully consistent with the theoretical discussion in Section 32–2, confirming the properties of plane mirrors as described in the text.

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Key Concepts

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

Magnification

Magnification is the ratio of the height of the image to the height of the object. In the case of mirrors, it is defined as the negative ratio of the image distance to the object distance. For plane mirrors, the magnification is always 1, meaning the image is the same size as the object, and it is virtual and upright.
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Plane Mirror Characteristics

A plane mirror is a flat reflective surface that produces images through reflection. The characteristics of images formed by plane mirrors include being virtual, upright, and of the same size as the object. The distance of the image from the mirror is equal to the distance of the object from the mirror, which is crucial for understanding magnification.
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Consistency with Theoretical Principles

In physics, consistency with theoretical principles means that experimental results align with established theories. In the context of plane mirrors, this involves verifying that the calculated magnification and image characteristics match the predictions made in the relevant sections of the textbook, ensuring a comprehensive understanding of the behavior of light and reflection.
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Related Practice
Textbook Question

A fish is swimming in water inside a thin spherical glass bowl of uniform thickness. Assuming the radius of curvature of the bowl is 32.0 cm, locate the image of the fish if the fish is located: (a) at the center of the bowl; (b) 20.0 cm from the side of the bowl between the observer and the center of the bowl. Assume the fish is small.

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Textbook Question

Two plane mirrors are facing each other 2.2 m apart as in Fig. 32–60. You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images of yourself. (a) How far away from you are the first three images of yourself in the mirror in front of you? (b) Are these first three images facing toward you or away from you?


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Textbook Question

(III) A beam of light enters the end of an optic fiber as shown in Fig. 32–59. (a) Show that we can guarantee total internal reflection at the side surface of the material (at point A), if the index of refraction is greater than about 1.42. In other words, regardless of the angle α , the light beam reflects back into the material at point A, assuming air outside. (b) What if the fiber is immersed in water?

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Textbook Question

Two identical concave mirrors are set facing each other 1.0 m apart. A small lightbulb is placed halfway between the mirrors. A small piece of paper placed just to the left of the bulb prevents light from the bulb from directly shining on the left mirror, but light reflected from the right mirror still reaches the left mirror. A good image of the bulb appears on the left side of the piece of paper. What is the focal length of the mirrors?

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Textbook Question

We wish to determine the depth of a swimming pool filled with water by measuring the width (x = 5.20m) and then noting that the bottom edge of the pool is just visible at an angle of 13.0° above the horizontal as shown in Fig. 32–61. Calculate the depth of the pool.


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Textbook Question

The critical angle of a certain piece of plastic in air is θC = 35.8°. What is the critical angle of the same plastic if it is immersed in water?

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