Answer to Question #208003 in Optics for Sanju

Question

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

Answer 1

Object distance, $u=-20\space m$

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

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

Height of image $=h'$

Image distance $= v$

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

$\dfrac{1}{v}=-\dfrac{1}{0.125}+\dfrac{1}{20}$

$v=-\dfrac{4}{3}\space m$

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

$h'=h\times\dfrac{-v}{u}$

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