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 distance of her face are 4 inch and 6 inch respectively. The minimum width of the required mirror is:

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

Answer 1

The correct option is D 5 inch


Eye to eye separation = CD = 4 inch
Ear to ear separation = AF = 6 inch
Now ray ABC from the left ear gets reflected from the plane mirror to the eyes C.
So, AB = BC = $\frac{AC}{2}$
Similarly, ED = EF = $\frac{DF}{2}$
So, minimum width of the mirror is,
BE = CD + BC + DE = 5 inch