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

Question

The writing on the passenger-side mirror of your car says "Warning! Objects in mirror are closer than they appear" (Figure 1) . 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 1.8-m-tall cyclist on a bicycle is 30 m from the mirror. You are 1.2 m from the mirror, and suppose, for simplicity, that the mirror, you, and the cyclist all lie along a line.

Part A: How far are you from the image of the cyclist?

Part B: How far would you have been from the image if the mirror were flat?

Part C: What is the image height?

Part D: What would the image height have been if the mirror were flat?

Explanation / Answer

A)From the lens eqn we know that

1/f = 1/i + 1/o

i = o x f / ( o - f)

i = 30 x -0.80 / (30 + 0.80) = -0.779 m

L = 1.2 + 0.779 = 1.98 m

Hence, L = 1.98 m

b)If the mirror were flat,

Lf = 1.2 + 30 = 31.2 m

Hence, Lf = 31.2 m

c)We know that,

M = -i/o = h'/h

h' = -i/o x h = 0.779/30 x 1.8 =0.047 m

Hence, image height = h' = 0.047 m = 4.7 cm

d)If the mirror were flat the height would have been equal to the object's height.

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