Answer to Question #200385 in Optics for Piolo

Question

What is the focal length of a makeup mirror that produces a magnification of 2.39 when a person’s face is 11 cm away?

answer to 3 decimal places

Answer 1

Given,

Magnification of the mirror $(m)=2.39$

Distance between the face and mirror $(u)=11cm$

Let the focal length of the mirror be f.

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

$\Rightarrow v=-11\times 2.39 cm$

$=-26.29cm$

Now, applying the mirror formula,

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

Now, substituting the values,

$\frac{1}{f}=\frac{-1}{26.29}+\frac{1}{11}$

$\Rightarrow \frac{1}{f}=\frac{-11+26.29}{11\times 26.29}$

$\Rightarrow \frac{1}{f}=\frac{15.29}{289.19}$

$\Rightarrow f = \frac{289.19}{15.29}$

$f=18.913cm$