How far are you from the image of the cyclist? The writing on the passenger-side

Question

How far are you from the image of the cyclist? 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 28 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. What is the image height? Express your answer using two significant figures. What would the image height have been if the mirror were flat? Express your answer using two significant figures.

Explanation / Answer

We know that from the mirror equation we get

1/f =1/di+1/do

1/-0.80 =1/di+1/28

Then the image distance is given by

1/di =-[1/0.80+1/28]=-[1.25+0.0357]=-1.2857

Therefore the image distance is di =-1/1.2857 =-0.777m behind the mirror

Then you are 1.4+0.777 =2.1778m from the image

But for the flat mirror the image is 28m behind. Therefore 1.4+28 =29.4m

Now from the magnification relation

hi/ho =di/do

hi/1.5 =0.777/28 ====>hi =(0.777/28)*1.5m =0.0416m

for the flat mirrors the image height is same as 1.5m

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