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A guy named Joe, who is 1.6 meters tall, enters a room in which someone has placed a large convex mirror with radius of curvature R equal to 30 meters. The mirror has been cut in half, so that the axis of the mirror is at ground level. (Figure 1) As Joe enters the room, he is 5 meters in front of the mirror, but he is looking the other way, so he fails to 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?
Express your answer in meters, to three significant figures or as a fraction.
Part B
What is the image height yim that Joe sees in the mirror?
Express your answer in meters, to three significant figures or as a fraction.
Part C
Now what is the length (i.e., the distance from head to toe) of Joe's image?
Express your answer in meters, to three significant figures or as a fraction.

Respuesta :

The ratio of object height to the image height is equal to the  object distance to the image distance.

  • A) The distance of the image appear to Joe is 8.75 meters.
  • B) The image height yim that Joe sees in the mirror 1.2 meters.
  • C) The length (i.e., the distance from head to toe) of Joe's image is 0.98 meters.

What is magnification ratio?

The ratio of object height to the image height is equal to the  object distance to the image distance. This ratio is called the magnification ratio.

Given information-

The height of the Joe is 1.6 meters.

The radius of curvature of convex mirror is 30 meters.

Joe is 5 meters in front of the mirror.

  • A) The distance of the image appear to Joe-

As the mirror is cut in the half. Thus the focus formula can be given as,

[tex]\dfrac{1}{f}=\dfrac{1}{-15}=\dfrac{1}{5}+\dfrac{1}{v} \\v=-3.75[/tex]

Negative sign indicates the image appears -3.75 behind the mirror.

Now the joe is standing 5 meters away from the mirror. Thus the distance of the image appear to Joe is,

[tex]d=5-(-3.75)\\d=8.75[/tex]

Thus the distance of the image appear to Joe is 8.75 meters.

  • B) The image height yim that Joe sees in the mirror.

The ratio of object height to the image height is equal to the  object distance to the image distance.

Suppose the height of the image is x meters. Thus,

[tex]\dfrac{1.6}{x}=\dfrac{5}{3.75}\\x=1.2 \rm m[/tex]

Thus, the image height yim that Joe sees in the mirror 1.2 meters.

  • C) The length (i.e., the distance from head to toe) of Joe's image.

As the Joe's head is 3.4 from the mirror Thus the formula for focus can be rewritten as,

[tex]\dfrac{1}{-15} =\dfrac{1}{3.4}+\dfrac{1}{v}\\v=-2.77\rm m[/tex]

Now the distance from the head to food can be find out as,

[tex]d=3.75-2.77\\d=0.98\rm m[/tex]

Thus, the length (i.e., the distance from head to toe) of Joe's image is 0.98 meters.

  • A) The distance of the image appear to Joe is 8.75 meters.
  • B) The image height yim that Joe sees in the mirror 1.2 meters.
  • C) The length (i.e., the distance from head to toe) of Joe's image is 0.98 meters.

Learn more about the magnificence ratio here;

https://brainly.com/question/2914376

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