At an intersection of hospital hallways, a con- vex mirror is mounted high on a

Question

At an intersection of hospital hallways, a con-
vex mirror is mounted high on a wall to help
people avoid collisions. The mirror has a ra-
dius of curvature of 0.559 m.
a. Locate the image of a patient from 22.6 m
the mirror.
Answer in units of m.

b. Find the magnification.

c.Describe the image.
1. virtual, inverted, smaller
2. virtual, upright, smaller
virtual, upright, larger
4. None of these
5. real, inverted, larger
6. real, upright, smaller
7. real, upright, larger
8. real, inverted, smaller
9. virtual, inverted, larger

Explanation / Answer

radius of curvature = r = -0.724m the center of curvature of convex mirroe behind the mirror as its focal length   so we set r = -0.559m so that focal length f = r/2                                   = -0.724m/2 = -0.362m the object is infront of the mirror d0 =18.7m from the mirror eq    1/di = 1/f - 1/d0          = 1/-0.362m - 1/18.7m    di = - 0.355m magnification m = -di/ d0                           = - ( -0.355m)/ 18.7m = 0.01898 image distance is negative so image is behind the mirror , image is up right and small                           = - ( -0.355m)/ 18.7m = 0.01898 image distance is negative so image is behind the mirror , image is up right and small

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