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The writing on the passengers-side mirror of your car says "Warning! Objects iin mirror are closer than they appear? this is no such warning on the driver's mirror
The writing on the passengers-side mirror of your car says "Warning! Objects iin mirror are closer than they appear? this 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 25 m from the mirror. You are 1.0m from the mirror, and suppose, for simplicity, that the mirror, you, and the cyclist all lie along a line.
A. how far are you from the image of the cyclist?
b. how far would you have been from the image if the mirror werre flat?
c. what is the image height?
d. What would the image height have been if the mirror were flat?
e why is there a label on the passenger side mirror?
Expert Solution
a
1/f = 1/di + 1/do
1/-0.80 = 1/di + 1/25
di = -0.775 m behind the mirror
so you are 1.0 + 0.775 = 1.775 m from the image
b
if flat mirror
the image would have been 25m behind so 1.0 + 25 = 26m
c
hi/ho = di/do
hi/1.5 = 0.775 / 25
hi = 0.0465 m
d
same as object so 1.5 m
e)
since our brains are not set up to compensate for convex mirrors
we would percieve the cyclist to be much farther away than he actually is
because the image is much smaller
to our eyes it's like we are looking in a flat mirror
the practical advantage to convex 'spot' mirrors
is the increased field of view
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