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The side mirrors on cars are convex mirrors. If the side mirror on the driver side of your car has a focal length with a magnitude of 5.40 m and a truck is at a distance of 3.00 m from the mirror, determine the following.

Required:
a. Image distance of the truck (Include the appropriate positive or negative sign.)
b. Magnification for this object distance (Include the appropriate positive or negative sign.)

Respuesta :

abidemiokin

Answer:

a) -1.93m

b) +0.643

Explanation:

Image distance and focal length of a convex mirror is negative.

a) Using the mirror formula to determine the image distance;

[tex]\frac{1}{f} = \frac{1}{u} +\frac{1}{v}[/tex]

f = focal length of the mirror = -5.40m

u = object distance from the mirror = 3.00m

v = image distance from the mirror

[tex]\frac{1}{-5.40} = \frac{1}{3} + \frac{1}{v}[/tex]

[tex]\frac{1}{v} = \frac{-1}{5.4} - \frac{1}{3}[/tex]

[tex]\frac{1}{v} = \frac{-1}{5.4} - \frac{1}{3}\\\frac{1}{v} = -0.1852 -0.3333\\\frac{1}{v} = - 0.5185\\v = \frac{-1}{0.5185} \\v = -1.93m[/tex]

b) Magnification = image distance/object distance

Magnification = 1.93/3

Magnification = +0.643

Note that we do not use the negative value of the image distance to calculate the magnification of the object

a. The  Image distance of the truck should be -1.93m.

b, The magnification of the object distance should be +0.643.

Calculation of the distance and the magnification:

here the mirror formula should be used

a.

1/f = 1/u + 1/v

where,

f = focal length of the mirror = -5.40m

u = object distance from the mirror = 3.00m

v = image distance from the mirror

So,

1/5.40 = 1/3 + 1/v

1/v = -1/5.4 - 1/3

So, v = -1.93m

b. Now the Magnification = image distance/object distance

= 1.93/3

= +0.643

learn more about distance here: https://brainly.com/question/21586135

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