Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
1st Edition
ISBN: 9781305259836
Author: Debora M. Katz
Publisher: Cengage Learning
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Chapter 37, Problem 31PQ
To determine

The object distance.

Expert Solution & Answer
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Answer to Problem 31PQ

The object distance is 1.20m.

Explanation of Solution

Write the expression for magnification produced by the mirror.

    m=did0=hih0

Here,m is the magnification produced by the mirror, d0 is the object distance, di is the image distance from the mirror, hi is the size of image and h0 for size of the object.

Rewrite the above equation to determine di.

    hih0=did0di=d0(hih0)                    (I)

Write the mirror equation for a convex mirror.

    1f=1d0+1di               (II)

Here, f is the focal length of the mirror.

Rewrite the equation (II) to determine f.

    1f=di+d0d0dif=d0didi+d0                      (III)

Conclusion:

Substitute 60.0cm for d0, h02 for hi in equation (I) to calculate di.

    di=(60.0cm)[h02h0]=(60.0cm)[12]=30.0cm

Substitute 30.0cm for di and 60.0cm for d0 in equation (III) to calculate f.

    f=(60.0cm)(30.0cm)30.0cm+60.0cm=60.0cm

Substitute h03 for hi in equation (I) to calculate di.

    di=d0[h03h0]=d0[13]=d03

Substitute 60.0cm for f and d03 for di in equation (II) to calculate do.

    160.0cm=1d0+1(d03)160.0cm=1d03d0160.0cm=1d0(13)60.0cm=d02

Simplify the above equation.

    60.0cm=d02d0=2×60.0cm=120.0cm(102cm1.0cm)=1.20m

Therefore, the object distance is 1.20m.

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Chapter 37 Solutions

Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics

Ch. 37 - Prob. 4PQCh. 37 - Prob. 5PQCh. 37 - Prob. 6PQCh. 37 - Prob. 7PQCh. 37 - Prob. 8PQCh. 37 - Prob. 9PQCh. 37 - Prob. 10PQCh. 37 - Prob. 11PQCh. 37 - Prob. 12PQCh. 37 - Prob. 13PQCh. 37 - Prob. 14PQCh. 37 - Light rays strike a plane mirror at an angle of...Ch. 37 - Prob. 16PQCh. 37 - Prob. 17PQCh. 37 - Prob. 18PQCh. 37 - Prob. 19PQCh. 37 - Prob. 20PQCh. 37 - Prob. 21PQCh. 37 - Prob. 22PQCh. 37 - Prob. 23PQCh. 37 - Prob. 24PQCh. 37 - Prob. 25PQCh. 37 - Prob. 26PQCh. 37 - Prob. 27PQCh. 37 - Prob. 28PQCh. 37 - A convex mirror with a radius of curvature of 25.0...Ch. 37 - The magnitude of the radius of curvature of a...Ch. 37 - Prob. 31PQCh. 37 - The image formed by a convex spherical mirror with...Ch. 37 - An object is placed 25.0 cm from the surface of a...Ch. 37 - Prob. 34PQCh. 37 - Prob. 35PQCh. 37 - Prob. 36PQCh. 37 - Prob. 37PQCh. 37 - Prob. 38PQCh. 37 - Prob. 39PQCh. 37 - Prob. 40PQCh. 37 - Prob. 41PQCh. 37 - Prob. 42PQCh. 37 - Prob. 43PQCh. 37 - Prob. 44PQCh. 37 - Prob. 45PQCh. 37 - Prob. 46PQCh. 37 - Prob. 47PQCh. 37 - Prob. 48PQCh. 37 - Prob. 49PQCh. 37 - Prob. 50PQCh. 37 - Prob. 51PQCh. 37 - Prob. 52PQCh. 37 - Prob. 53PQCh. 37 - Prob. 54PQCh. 37 - Prob. 55PQCh. 37 - Prob. 56PQCh. 37 - You see the image of a sign through a camera...Ch. 37 - Prob. 58PQCh. 37 - Prob. 59PQCh. 37 - Prob. 60PQCh. 37 - An object is placed midway between two concave...Ch. 37 - Prob. 62PQCh. 37 - Prob. 63PQCh. 37 - Prob. 64PQCh. 37 - Prob. 65PQCh. 37 - Prob. 66PQCh. 37 - Observe your reflection in the back of a spoon....Ch. 37 - Prob. 68PQCh. 37 - A small convex mirror and a large concave mirror...Ch. 37 - Prob. 70PQCh. 37 - Prob. 71PQCh. 37 - Prob. 72PQCh. 37 - Prob. 73PQ
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