(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 = 16 cm) to scale, and place an object 26 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)

(e) What is the ratio of the image height when the object distance is 5 cm to that when the object distance is 26 cm? Give your answer to one significant figure.

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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 = -8cm

Do = 26cm

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 = -6.1177cm
Images are formed behind convex mirrors so the answer is:
6.1cm behind the convex mirror

Now for finding the height of the image we need the Magnification equation
M = -Di/Do = Hi/Ho
M = -(-6.1177cm)/(26cm) = Hi/(4cm)
Solve for Hi
Hi = 0.9411cm

b)
Same thing as before except now Do = 5cm
Using the focal length equation
Di = -3.0769cm
3.0769cm behind the mirror
Using the magnification equation
Hi = 2.46cm

c)
2.46cm / 0.9411cm = 2.6
Change to one significant figure 3

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