EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
1st Edition
ISBN: 9780100546714
Author: Katz
Publisher: YUZU
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Chapter 37, Problem 15PQ

Light rays strike a plane mirror at an angle of 45.0° as shown in Figure P37.15. At what angle should a second mirror be placed so that the reflected rays are parallel to the first mirror?

Chapter 37, Problem 15PQ, Light rays strike a plane mirror at an angle of 45.0 as shown in Figure P37.15. At what angle should

Expert Solution & Answer
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To determine

The angle at which the second mirror be placed so that the reflected rays are parallel to the first mirror.

Answer to Problem 15PQ

The angle at which the second mirror be placed so that the reflected rays are parallel to the first mirror is 67.50°.

Explanation of Solution

The following figure shows the reflection diagram.

EBK PHYSICS FOR SCIENTISTS AND ENGINEER, Chapter 37, Problem 15PQ

Figure-(1)

Here, θi is the incident angle, θr is the refracted angle, θ is the angle of the second mirror with the first mirror, ϕi is the angle of reflected light ray from the first mirror with the second mirror, and ϕr is the angle of the reflected light ray from the second mirror with the second mirror.

Calculate the angle from the above diagram.

    θi+45.0°=90.0°θi=90.0°45.0°=45.0°

According to law of reflection θi=θr. Hence,

    θr=45.0°

Calculate the other angles from the above diagram.

    θr+γr=90.0°                                                                                      (I)

From the above figure, the total angle in the triangle ABC is equal to 180°.

    θr+2θi+90.0°=180.0°                                                                          (II)

For the second mirror, the total angle in a straight line is equal to 180°.

    2θi+ϕi+ϕr=180.0°                                                                           (III)

From the above figure, the total angle in the triangle ACD is equal to 180°.

    θ+ϕi+γr=180.0°                                                                               (IV)

Conclusion:

Substitute 45.0° for θr in equation (I) to calculate γr.

    45.0°+γr=90.0°γr=90.0°45.0°γr=45.0°

Substitute 45.0° for θr in equation (II) and solve for 2θi.

    45.0°+2θi+90.0°=180.0°2θi=180.0°90.0°45.0°2θi=45.0°

Substitute 45.0° for 2θi and ϕi for ϕr in equation (III) to calculate ϕi.

    45.0°+ϕi+ϕi=180.0°2ϕi=180.0°45.0°ϕi=180.0°45.0°2ϕi=67.50°

Substitute 45.0° for γr, and 67.50° for ϕi in equation (IV) to calculate θ.

    45.0°+θ+67.50°=180.0°θ=180.0°67.50°45.0°θ=67.50°

Therefore, the angle at which the second mirror be placed so that the reflected rays are parallel to the first mirror is 67.50°.

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Chapter 37 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

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