   Chapter 34, Problem 4P Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Solutions

Chapter
Section Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

A dance hall is built without pillars and with a horizontal ceiling 7.20 m above the floor. A mirror is fastened flat against one section of the ceiling. Following an earthquake, the mirror is in place and unbroken. An engineer makes a quick check of whether the ceiling is sagging by directing a vertical beam of laser light up at the mirror and observing its reflection on the floor. (a) Show that if the mirror has rotated to make an angle ϕ with the horizontal, the normal to the mirror makes an angle ϕ with the vertical. (b) Show that the reflected laser light makes an angle 2ϕ with the vertical. (c) Assume the reflected laser light makes a spot on the floor 1.40 cm away from the point vertically below the laser. Find the angle ϕ.

(a)

To determine

To show: The normal to the mirror makes an angle ϕ with the vertical if the mirror has rotated to make an angle ϕ with the horizontal.

Explanation

Given info:  The mirror has rotated an angle ϕ with the horizontal.

Figure (1)

The figure (1) shows a plane-mirror and a fixed incident ray of light reflecting from the surface at an angle θ .

From, law of reflection the angle of incidence is equal to the angle of reflection.

θi=θr (1)

Here,

θi is the angle of incidence.

θr is the angle of reflection.

The mirror is rotated through an angle ϕ

(b)

To determine

To show: The reflected laser light makes an angle 2ϕ with the vertical.

(c)

To determine
The angle ϕ if the reflected laser light makes a spot on the floor 1.40cm away from the point vertically below the laser.

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