Question #200385

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


1
Expert's answer
2021-06-03T13:51:40-0400

Given,

Magnification of the mirror (m)=2.39(m)=2.39

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

Let the focal length of the mirror be f.

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

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

=26.29cm=-26.29cm

Now, applying the mirror formula,

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

Now, substituting the values,

1f=126.29+111\frac{1}{f}=\frac{-1}{26.29}+\frac{1}{11}


1f=11+26.2911×26.29\Rightarrow \frac{1}{f}=\frac{-11+26.29}{11\times 26.29}


1f=15.29289.19\Rightarrow \frac{1}{f}=\frac{15.29}{289.19}


f=289.1915.29\Rightarrow f = \frac{289.19}{15.29}


f=18.913cmf=18.913cm


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