# You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be : Option 1) 30 cm Option 2) 24 cm Option 3) 60 cm Option 4) -24 cm

As we learnt in

Mirror Formula -

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

- wherein

$u=$ Object distance from pole of mirror.

$v=$ Image distance from pole of mirror.

$f=$ focal length of the mirror.

Relation between focal length and radius of curvature -

$f=\frac{R}{2}$

- wherein

This is valid only for smaller angle of incidence.

i.e.paraxial rays

From question v = 15 cm,  u = -10 cm

Radius of curvature R = 2f = ?

Mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}=\frac{1}{15}+\frac{1}{(-10)}=\frac{1}{f}$

f = - 30 cm

$\therefore$    R= 2(-30) = - 60 cm

Correct option is 3.

Option 1)

30 cm

This is an incorrect option.

Option 2)

24 cm

This is an incorrect option.

Option 3)

60 cm

This is the correct option.

Option 4)

-24 cm

This is an incorrect option.

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