A guy named Joe, who is 1.6 meters tall, enters a room in which someone has placed a large convex mirror with?
A man named Joe, who is 1.6 meters tall, enters a room where a large convex mirror has been placed. The mirror has a radius of curvature (R) of 30 meters and has been cut in half, with its axis positioned at ground level. As Joe enters the room, he is 5 meters in front of the mirror but is looking the other way, so he does not see it. When he turns around, he is startled by his own image in the mirror.
Part A: How far away does the image appear to Joe? (The correct answer is 8.75 m.)
Part B: What is the height of Joe's image that he sees in the mirror? (The correct answer is 1.2 m.)
Joe is so startled by his image that he falls forward, assuming his feet remain in the same position.
Part C: What is the length (i.e., the distance from head to toe) of Joe's image? How do you find the answer to Part C?
Figure 1: http://session.masteringphysics.com/problemAsset/1...
Figure 2: http://session.masteringphysics.com/problemAsset/1...
4 Answers
A) 1/f = 1/–15 = 1/5 + 1/v
v = – 3.75 m ( That is 3.75 m behind the mirror = 8.75 m from Joe )
B) Object height / Image height = Object distance / Image distance
Image height = 1.6 . 3.75 / 5 = 1.2 m
C) Joe's head is now 3.4 m from the mirror
1/–15 = 1/3.4 + 1/v
v (head ) = – 2.77 m
Distance from head to foot of the image is
3.75 – 2.77 = 0.98 m
Hello
I get - or you can get - your first answer to - how far is the image from Joe - from
I/O = di/do = (r - di)/(r + do)
di/5 = (30 - di)/( 30 + 5)
35 di = 150 - 5 di
40 di = 150
di = 3,75 m (this is behind the mirror, and this distance plus 5 m which Joe is before the mirror = 8,75 m.
Now use the same equation for his head, which has a distance of 5 - 1,6 m = 3,4 m from the mirror.
What is the distance of the image of the head behind the mirror:
di/3,4 = (30 - di) / (30 + 3,4)
33,4 di = 102 - 3,4 di
36,8 di = 102
di = 2,77174 m
Since the image of the feet was 3,75 m behind the mirror,
the length of the image of his body is 3,75 - 2,7717 m
= 0,978 m.
Regards
Edit
you can also get di from
1/di + 1/do = 1/-f ( here is f = - f, because it is behind the mirror, and f = -1/2 r )
1/di = - 1/15 - 1/do
1/di = - 1/15 - 1/3,4
1/di = (- 3,4 - 15)/(3,415) = - 18,4/(3,415)
di = 2,771739 m
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