Question

A person has a 15cm wide face and his two eyes are separated by 9cm. The minimum width of a mirror required for the person to view his complete face literally is
A. 15cm
B. 9cm
C. 6cm
D. 3cm

Answer 1

Hint: The minimum width of a mirror required for the person to view his complete face will be $\dfrac{{\left( {W - w} \right)}}{2}$, where W is the width of his face and w is the distance separating his eyes. Substitute the values and find the required width of the mirror.

Complete step by step answer:
We are given that a person has a 15cm wide face and his two eyes are separated by 9cm.
We have to calculate the minimum width of the mirror required for the person to view his complete face.
The width of the person’s face (W) is 15cm.
The distance between his eyes (w) is 9cm.
Minimum mirror width (d) will be
$
  d = \dfrac{{W - w}}{2} \\
  W = 15cm,w = 9cm \\
  d = \dfrac{{15 - 9}}{2} \\
\implies d = \dfrac{6}{2} \\
\therefore d = 3cm \\
 $
Therefore, the minimum width of the mirror should be 3cm.
A mirror of minimum width 3cm is required for a person with a face 15cm wide and 9cm wide separation between his eyes.

So, the correct answer is “Option D”.

Additional Information:
There are three types of mirrors i.e. plane mirror, concave mirror and convex mirror. Plane mirrors are flat and smooth; Concave mirrors are spherical mirrors which are bent inwards; convex mirrors are also spherical mirrors which are bent outwards.

Note:
Light goes through and gets refracted by a Lens whereas light gets reflected by a mirror. A mirror has one focal point whereas a lens will have two focal points either side of the lens. Images are formed using mirrors and light is bent using lenses. Don’t be confused with a lens and a mirror.