A dance hall is built without pillars and with a horizontal ceiling 7.40 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.

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A dance hall is built without pillars and with a horizontal ceiling 7.40 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 phi with the horizontal, the normal to the mirror makes an angle phi with the vertical. 
(b) Show that the reflected laser light makes an angle 2phi with the vertical. 
(c) If the reflected laser light makes a spot on the floor 2.20 cm away from the point vertically below the laser, find the angle phi
 °
asked Apr 2, 2012 in Physics by Gummmys ~Expert~ (1,105 points)
    

1 Answer

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Best answer

*Parts A and B, textbook solution:

Part A:

Let AB be the originally horizontal ceiling, BC its originally vertical normal, AD the new ceiling and DE its normal. Then the angle BAD = phi. By definition DE is perpendicular to AD and BC is perpendicular to AB. Then the angle between DE extended and BC is phi because angles are equal when their sides are perpendicular, right side to right side and left side to left side.

Part B:

Now CBE = phi is the angle of incidence of the vertical light beam. Its angle of reflection is also phi. The angle between the vertical incident beam and the reflected beam is 2phi.

 

 

Part C:

Using the geometry of the triangle you set up the following relation:

 

tan(2phi) = y / x  = 2.2 cm / 740 cm

 

answered Apr 5, 2012 by Joey33 ~Expert~ (1,216 points)
selected Apr 9, 2012 by Gummmys

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