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a mirror on the passenger side of your car is convex and has a radius of curvature with magnitude 18.0 cm. (a) another car is behind your car, 9.00 m from the mirror, and this car is viewed in the mirror by your passenger. if this car is 1.5 m tall, what is the height of the image? (b) the mirror has a warning attached that objects viewed in it are closer than they appear. why is this so?

User JWK
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1 Answer

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(a) The height of the image is 1.5 cm.

(b) The warning is due to convex mirror's ability to diverge light rays, making objects appear smaller and farther away than they actually are.

How to calculate the image distance?

The image distance is calculated by applying the following formula as follows;

-1/f = 1/u + 1/v

where;

  • f is the focal length
  • u is the object distance = 9m = 900 cm
  • v is the image distance = ?

The focal length = r/2

f = 18 cm / 2

f = 9 cm

-1/9 = 1/900 + 1/v

1/v = -1/9 - 1/900

1/v = -0.1122

v = 1/(-0.1122)

v = -8.9 cm

(a) The height of the image is calculated as;

M = Hi/h = v/u

Hi/1.5 = 8.9 / 900

Hi = 1.5 x (8.9/900)

Hi = 0.015 m

Hi = 1.5 cm

(b) The warning on the mirror ("objects are closer than they appear") is due to the convex mirror's ability to provide a wider field of view. Convex mirrors diverge light rays, making objects appear smaller and farther away than they actually are.

User StevGates
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