At an intersection of hospital hallways, a convex mirror is mounted high on a wa

Question

At an intersection of hospital hallways, a convex mirror is mounted high on a wall to help people avoid collisions. The mirror has a radius of curvature of 0.453 m.

a.) Locate the image of a patient from 19.1 m the mirror. Answer in units of m.

b.) Find the magnification.

c. Describe the image.

1. real, upright, smaller

2. None of these

3. real, upright, larger

4. virtual, upright, larger

5. virtual, inverted, larger

6. virtual, inverted, smaller

7. real, inverted, larger

8. real, inverted, smaller

9. virtual, upright, smaller

Explanation / Answer

Here,

radius of curvature = 0.453 m

focal length , f = -0.453/2 m

f = -0.227 m

object distance , do = 19.1 m

a) let the image position is di

Using lens formula

1/f = 1/di + 1/do

-1/.227 = 1/di + 1/19.1

di = -0.224 m

the image is located at -0.224 m from the mirror

b)

magnification = -di/do

magnification = 0.224/19.1

magnification = 0.0117

c)

as the magnification is positive and less than 1

the image is 6. virtual, inverted, smaller

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