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Suppose a man stands in front of a mirror as shown in

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs ISBN: 9781938168000 42

Solution for problem 1PE Chapter 25

College Physics | 1st Edition

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College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

College Physics | 1st Edition

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Problem 1PE

Suppose a man stands in front of a mirror as shown in Figure 25.50. His eyes are 1.65 m above the floor, and the top of his head is 0.13 m higher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. How is this distance related to the man’s height?

                

Figure 25.50 A full-length mirror is one in which you can see all of yourself. It need not be as big as you, and its size is independent of your distance from it.

Step-by-Step Solution:
Step 1 of 3

Solution 1PE

By the law of reflection and ray tracing, the angle of incidence is equal to the angle of reflection, so the top of the mirror must extend to at least halfway between his eyes and the top of his head and the bottom must go down to halfway between his eyes and the floor. This result is independent of how far person stands from the wall.

a  = b / h

a  =  m

a  = 0.065 m

b  = m

b  = 0.825  m

h  =  1.65 + 0.13 m

h  = 1.78 m

 the length of the mirror L is

L = h= (a +b)

L = 0.89 m

bottom of the smallest mirror is,

b  = 0.825 m

 top of the mirror from the floor is

b +L = 1.715 m

 the floor the bottom of smallest mirror is   0.825 m and top is 1.715 m and height of the mirror is 0.89 m  precisely one-half the height of the person.

Step 2 of 3

Chapter 25, Problem 1PE is Solved
Step 3 of 3

Textbook: College Physics
Edition: 1
Author: Paul Peter Urone, Roger Hinrichs
ISBN: 9781938168000

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Suppose a man stands in front of a mirror as shown in