Problem 18.77 The writing on the passenger-side mirror of your car says \"Warnin
ID: 1402414 • Letter: P
Question
Problem 18.77
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 1.6-m-tall cyclist on a bicycle is 29 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.
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 1.6-m-tall cyclist on a bicycle is 29 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?
Express your answer to two significant figures and include the appropriate units.
L = ___________
Part B
How far would you have been from the image if the mirror were flat?
Express your answer to two significant figures and include the appropriate units.
Lf= ________________
Part C
What is the image height?
Express your answer to two significant figures and include the appropriate units.
h`= ___________
Part D
What would the image height have been if the mirror were flat?
Express your answer to two significant figures and include the appropriate units.
h`f = ____________
Explanation / Answer
given object distane from the mirro = s = 29 m
focal length f = -80 cm
image distance from the covex mirror = s' = ?
from mirror equation
1/s + 1/s' = 1/f
1/29 + 1/s' = -1/0.80
s' = -(29*0.8))/(29+0.8) m
s' = -0.78m <<----answer
distance of the image from you = 0.78+1.2 = 1.98 m <<----answer
part(B)
if the mirro is flat
s' = s = 29 m
distance of the mirror from you = 29+1.2 = 30.2 m <<----answer
part(C)
y'/ y = s'/s
y' = s'*y/s
y' = (0.78*1.6)/29
y' = 0.043 m
part(D)
the distance of the image from the mirror = s' = 29 m
from you
hf/1.2 = 1.6/(29+1.2)
hf = (1.2*1.6)/(29+1.2)
hf = 0.064 m <<----answer