14. (28 points) DO THIS PROBLEM LAST AS IT MAY TAKE SOME TIME TO COMPLETE. You
are at an amusement park with your friends and go into the "House of Mirrors". Once you enter, the
first thing you see is two flat mirrors nearly parallel to each other, 5 meters apart. When you step
between them, you turn to face the nearest mirror (on the right), which is 2 m from your face. Looking
toward this mirror, you first see your face and then, farther away in the mirror, the back of your head.
(The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can
treat them as parallel for this problem).
a. Draw a sketch of this situation, labeling all that you know. Consider you are facing to the
right. NOTE – you will be adding more to this sketch in the following sections.
b. At what distance does the image of your face (image 1) appear according to the mirror in
front of you (on the right)? Also place and label it on your sketch.
c. How far away are you from the image of your face in the mirror on the right?
d. As you continue to look in the mirror on the right, you say to your friend Alex, who is
also room with you, "Look I can see the reflection of the back of my head from the
mirror behind us!"
a. Where does the image of the back of your head (image 2) appear according to the
mirror behind you (on the left)? Place and label it on your sketch.
b. How far away from the mirror behind you does the image of the back of your
head appear?
c. You see the reflected image (image 3) of the back of your head in the mirror on
the right (the one you are facing). Place and label it on your sketch.
d. How far away from the mirror on the right does image 3 appear to be according to
the mirror you are facing? (Neglect the thickness of your head).