The writing on the passenger-side mirror of your car says \"Warning! Objects are

Question

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 24 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 angular size of the image of the cyclist?

What would the angular size of the cyclist's image have been if the mirror were flat?

Explanation / Answer

a) 1/f = 1/di + 1/do
1/-0.80 = 1/di + 1/24
di = -0.774 m behind the mirror
so you are 1.4 + 0.774 = 2.174 m from the image

if flat mirror the image would have been 24 m behind so 1.4 + 24 = 25.4m

hi/ho = di/do
hi/1.5 = 0.774 / 24  = 0.03225 m

angle size = 2(arctan (1/2 hi/d) ) = 2(arctan(2*0.03225/2.174) ) = 3.4°

b) same as object so 1.5 m

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