(a) An object is placed in front of a convex mirror. Draw a convex mirror (radiu

Question

(a) An object is placed in front of a convex mirror. Draw a convex mirror (radius of curvature = 12 cm) to scale, and place an object 34 cm in front of it. Make the object height 4 cm. Using a ray diagram, locate the image and measure its height. (Do this diagram on paper. Your instructor may ask you to turn in this work.)
____cm (image location, include sign)
____cm (image height, include sign)

(b) Now move the object closer to the mirror, so the object distance is 5 cm. Again, locate its image using a ray diagram.
_____cm (image location, include sign)
_____cm (image height, include sign)

(c) As the object moves closer to the mirror, does the magnitude of the image distance become larger or smaller?

(d) As the object moves closer to the mirror, does the magnitude of the image height become larger or smaller?

(e) What is the ratio of the image height when the object distance is 5 cm to that when the object distance is 34 cm? Give your answer to one significant figure.
h5 cm / h34 cm =

Explanation / Answer

a)
Focal length, F
Distance of Object from mirror, Do
Distance of Image from mirror, Di
Magnification, M
Height of Object, Ho
Height of Image, Hi

The focal length is half of the radius of curvature and is negative since it is a convex mirror.
F = - 6 cm

Do = 34 cm

The equation relating F, Do, and Di is
1/F = 1/Do + 1/Di
Solve for Di while plugging in the values for F and Do you get
Di = - 5.37cm
Images are formed behind convex mirrors so the answer is:
5.37 cm behind the convex mirror

Now for finding the height of the image we need the Magnification equation
M = -Di/Do = Hi/Ho
M = -(-5.37cm)/(34cm) = Hi / (4cm)
Solve for Hi
Hi = 0.63 cm.

b)
Same thing as before except now Do = 5cm
Using the focal length equation
Di = - 2.72cm
3.15cm behind the mirror
Using the magnification equation

M = -Di/Do = Hi/Ho
M = -(-2.72cm)/(34cm) = Hi/(4cm)
Solve for Hi
Hi = 0.32 cm.

e)

0.32cm / 0.63cm = 0.51

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