Question

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

• A. $1inch$
• B. $2inch$
• C. $2.5inch$
• D. $5inch$

Answer 1

The correct option is D $5inch$

Eye to eye separation $=BD=4inch$

Ear to ear separation $=AE=6inch$

Now ray ABC is from the left ear gets reflected from the plane mirror to the eyes C.

So, $AB=BC=\frac{AC}{2}$

Similarly $DE=EF=\frac{DF}{2}$

So minimum width of the mirror is, $=BE=CD+BC+DE=5inch$