The writing on the passenger-side mirror of your car says "warning! objects are closer than they appear." there is no such warning on the driver's mirror. consider a typical convex passenger-side mirror with a focal length of -80 cm . a 1.5 m -tall cyclist on a bicycle is 30 m from the mirror. you are 1.4 m from the mirror, and suppose, for simplicity, that the mirror, you, and the cyclist all lie along a line.
- you are 2.2 m from the image of the cyclist
a) what is the image height?
b) what would the image height have been if the mirror were flat?
c) what is the angular size of the image of the cyclist?
d) what would the angular size of the cyclist's image have been if the mirror were flat?
e) explain why is there a warning label on the passenger-side mirror?

image height = 0.1  m

image height if flat mirror 1.5 m

θ =  2.86 degree

θ  if flat mirror  =  41.10 degree

warning label  because image is small than object

Explanation:

given data

focal length = -80 cm = 0.80 m

tall = 1.5 m

cycle distance  d1 = 30 m

we from mirror distance = 1.4 m

image of cyclist d2 = 2.2 m

to find out

image height ,  image height if mirror flat , angular size , angular size if mirror flat and why is there a warning label

solution

we apply here formula

image height / tall =  d2 / d1

image height / 1.5 =  2 / 30

image height = 0.1  m

and

image height if mirror flat

so height will be same as object height 1.5 m

and

angular size image formula is

θ =  2tan^-1 ( image height /2d2)

θ =  2tan^-1 ( 0.1 /2(2) )

θ =  2.86 degree

and if mirror is flat

angular size

θ =  2tan^-1 ( image height /2d2)

θ =  2tan^-1 ( 1.5 /2(2) )

θ =  41.10 degree

and

we know image is small than object so we can think object is large distance than in real so if we stop instantly so other person will be surprised he have time to stop vehicle

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