Question

A toy car is placed 29.0cm from a convex mirror. The image of the car is upright and one-sixth as large as the actual car. Calculate the mirror's power in diopters.

Answer 1

Answer:

The power of the mirror is -17.24 diopter.

Explanation:

Magnification of an image,m = $\frac{1}{6}$

Distance of the object from the mirror = u = 29.0 cm

Distance of an image from the mirror = v

Magnification = $m=\frac{-v}{u}$

$\frac{1}{6}=\frac{-v}{u}$

$v=\frac{-u}{6}$

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

$\frac{1}{f}=\frac{1}{u}+\frac{-6}{u}$

$f=\frac{-u}{5}=\frac{-29.0 cm}{5}=-5.8 cm$

Focal length of mirror = -5.8 cm =-0.058 m

Power of the lens = P

$P =\frac{1}{f}$

$P=\frac{1}{-0.058 m}=-17.24 D$