Question

A concave makeup mirror has a radius of curvature of 50 cm. It is positioned so that when a person looks in the mirror, they see their face upright and 2.6 times larger. How far is the mirror from the face? a) 9.23 cm b) 13.5 cm c) 11.1 cm d) 15.4 cm e) 17.8 cm

Answer 1

d) 15.4 cm

Step-by-step explanation:

Radius of curvature = 50 cm

i = image distance

o = object distance

Focal length (f) is half of radius of curvature

So f = 25 cm

Magnification = m = 2.6

`m=-(i)/(o)\\\Rightarrow i=-2.6o`

Mirror equation

`(1)/(i)+(1)/(o)=(1)/(f)\\\Rightarrow (1)/(-2.6o)+(1)/(o)=(1)/(25)\\\Rightarrow (-1+2.6)/(2.6o)=(1)/(25)\\\Rightarrow (1.6)/(2.6o)=(1)/(25)\\\Rightarrow 25=(2.6o)/(1.6)\\\Rightarrow 25=1.625o\\\Rightarrow o=(25)/(1.625)\\\Rightarrow o=15.38\ cm`

Object distance is 15.4 cm