Question

A beautiful girl with two normal eyes wants to see full width of her face by a plane mirror. The eye to eye and ear to ear distances of her face at $4$ inch and $6$ inch respectively. The minimum width of the required mirror is

• A. $1$ inch
• B. $2$ inch
• C. $3$ inch
• D. $4$ inch

Answer 1

The correct option is A $1$ inch

The image of the right ear will be seen in the left eye and that of the left ear will be seen in the right eye.

The minimum length of the mirror required is as shown in the diagram. The length of the mirror will be AB.

So, $AC$ $=3-\frac{5}{2}$ $=\frac{1}{2}$inch

So, $CB$ $=3-\frac{5}{2}$ $=\frac{1}{2}$inch

So, $A$ and $B$ both are $\frac{1}{2}$inch from center $C$.

So, $AB$ $=1$ inch
So, minimum width of the required mirror is $1$ inch.