Question #208003

A car is at a distance 20 m in front of a convex car-mirror having a focal length f = -0.125 m. If the height of the car is 1.45 m, how tall is its image?


h = 0.95 cm


h=1.51 cm


h = 0.76 cm


h = 0.90 cm


h=1.01 cm


1
Expert's answer
2021-06-17T15:07:30-0400

Object distance, u=20 mu=-20\space m

Focal length of car, f=0.125 mf=-0.125\space m

Height of object, h=1.45 mh=1.45\space m

Height of image =h=h'

Image distance =v= v

1f=1v+1u\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}

1v=10.125+120\dfrac{1}{v}=-\dfrac{1}{0.125}+\dfrac{1}{20}

v=43 mv=-\dfrac{4}{3}\space m

Magnification, m=hh=vum=\dfrac{h'}{h}=-\dfrac{v}{u}

h=h×vuh'=h\times\dfrac{-v}{u}

h=0.09666 m0.95 cmh'=-0.09666\space m\approx0.95\space cm


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