Question

A beautiful girl with two normal eyes wants to see the full width of her face by a plane mirror. The eye to eye and ear to ear distances of her face at $4inch$ and $6inch$ respectively. The minimum width of the required mirror is
A. $1inch$
B. $2inch$
C. $3inch$
D. $4inch$

Answer 1

Hint: You can start by briefly explaining what the situation given in the problem is and what condition that the width of the mirror should satisfy, i.e. the left eye should be able to see the right ear and the right ear should be able to see the left ear. Then draw a diagram based on this and find the width of the plane mirror.

Complete step by step answer:
Here in the problem we are given that a beautiful girl with two normal eyes wants to see the full width of her face in a plane mirror. The full width of her face means that the left eye should be able to see the right ear and the right ear should be able to see the left ear.
Let’s draw a diagram that satisfies the above conditions.

Here we have multiple triangles, but we just have to focus on $\Delta ACG$ . So for $\Delta ACG$ the point $B$ is the middle point of the base $AG$ .
So $AB = \dfrac{{AG}}{2}$
$AB = \dfrac{5}{2}inch$
We also know that $AD = 1 + 2 = 3inch$
So from the diagram we can see that
$BD = CE = AD - AB$
$CE = 3 - \dfrac{5}{2}$
$CE = \dfrac{1}{2}inch$
Similarly we can also say that $EF = \dfrac{1}{2}$ .
So the size of the mirror is
$CF = CE + EF$
$CF = \dfrac{1}{2} + \dfrac{1}{2}$
$CF = 1 inch$
Hence, the plane mirror should be $1 inch$ in width.
Hence, the correct answer is option A.

Note:
Plane mirror is essentially a rectangular glass slab with a really smooth surface and is coated on one side by silver. Plane mirrors always produce an upright, virtual image. The size of the image is the same size as the object. The distance of the image from the plane mirror is the same as the distance of the object from the mirror.