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Suppose a man stands in front of a mirror as shown in Figure $25.49 .$ His eyes are 1.65 mabove 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?

The top of the mirror has to be 1.715 $\mathrm{m}$ above the floor and the bottom has to be 0.825 $\mathrm{m}$ above the floor.

Physics 103

Chapter 25

Geometric Optics

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

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So here's the situation. We have a person here. We're standing in front ofa. I mean, we're which is awful. And l eso his eyes up to his eyes from the Florida of years, the floor up to his eyes. The height is the 1.65 meter and from ice to top off his head. Here he is. 3.1. Meet three meters, um, meter from the floor to here. Easy. Um, from here is a B, and from here, up to this top is hey, um, the top mirror must extend to it least halfway between the eyes and the top of the head. The bottom must go down the halfway between his eyes in the floor. Uh, this result is independent off how, how far he stands from the mirrors. This is independent off that. So then able Britain is here from the Elberton is 0.13 meter divided by two. That he's ah 0.65 meter. And the big evil Burton is 1.65 mutually way to this. With us zero point it to fund future, Um, then l will be equal to 1.65 meter plus little 0.13 nature minus a minus B. So simplifying this we get here, um, substituting the value off and be off course, we get here of 0.89 meter. The bottom is a B, which is, um is there a 0.8 to 5 from the floor and the top will be top will be B plus l. So from here be in the dope will be B plus il, which is equal to their 0.8 to 5 plus some little 0.8 night. This gives us 1.715 meter from the floor from the floor, so the top off the mirror will be 1.75 meters from

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