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

Giancoli Douglas 5th edition

Ch. 32 - Light: Reflection and Refraction

Problem 70

Chapter 31, Problem 70

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?

<IMAGE>

Verified step by step guidance

Identify the distances for the first three images formed by the mirror in front of you. The first image is formed by the direct reflection from the mirror you are facing. The distance to this image is simply twice the distance you stand from the mirror, as the light travels to the mirror and back to you.

For the second image, consider the reflection from the opposite mirror. The light travels from you to the mirror in front of you, reflects, travels to the opposite mirror, reflects back to the first mirror, and then reflects back to you. Calculate this total distance by adding up these segments.

For the third image, the light path involves an additional round trip to the opposite mirror and back to the first mirror before reflecting back to you. Sum up these distances to find the total path length for the third image.

To determine the orientation of each image, recall that each reflection in a plane mirror reverses the orientation. Count the number of reflections for each image: an odd number of reflections results in an image facing toward you, while an even number results in an image facing away from you.

Apply the reflection count to each of the first three images to determine whether they are facing toward you or away from you.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Reflection of Light

Reflection of light occurs when light rays bounce off a surface, such as a mirror. The angle of incidence, which is the angle between the incoming ray and the normal (a line perpendicular to the surface), equals the angle of reflection. This principle is crucial for understanding how images are formed in mirrors, as it determines the path of light rays and the location of images relative to the observer.

Image Formation in Mirrors

When light reflects off a plane mirror, it creates virtual images that appear to be behind the mirror. The distance of the image from the mirror is equal to the distance of the object from the mirror. In the case of two mirrors facing each other, multiple reflections can occur, leading to the formation of several images, each appearing at different distances from the observer.

Multiple Images from Parallel Mirrors

When two parallel mirrors are placed facing each other, they create a series of images due to repeated reflections. The first image appears directly behind the first mirror, while subsequent images are formed by reflections of the previous images. The distance of these images can be calculated based on the distance between the mirrors and the observer's position, leading to a pattern of images that can be analyzed mathematically.

Recommended video:

06:06

Ray Diagrams for Plane Mirrors

Related Practice

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?

Textbook Question

(d) Are your results in parts (b) and (c) consistent with the discussion of Section 32–2 on plane mirrors?

views

Textbook Question

A 1.80-m-tall person stands 4.20 m from a convex mirror and notices that he looks precisely half as tall as he does in a plane mirror placed at the same distance. What is the radius of curvature of the convex mirror? (Assume that θ ≈ θ .) [Hint: The viewing angle is half.]

views

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.

<IMAGE>

views

Textbook Question

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

views

Textbook Question

The label on a laser says it produces light of wavelength 670 nm. The laser beam passes through a block of plastic for which n = 1.57. What is the wavelength of the light inside the plastic?

views