Question

A person has a $18$cm wide face and his two eyes are separated by 8 cm.Find the minimum width of a mirror required for the person to view is face laterally is

• A. $9$cm
• B. $4$cm
• C. $5$cm
• D. $13$cm

Answer 1

The correct option is C $5$cm

For minimum width -

i). Center of face and mirror must lie in perpendicular bisector of the line joining two eyes.

ii). Left eye must see right end point of face at the end of the mirror.

iii). Night eye must see left end point of face at then end of the mirror.

Now let,

$F_1,F_2$ end points of face width $11E_1,E_2$ two eyes $11C-$ center of face.

$m_1.m_2-$ mirror end points

$m_1,m_2-$ projection of $m_1{m}_2$ on line joining two eyes.

Now, line joining two eyes should look like -

$F_1--E_1---m_1-C---m_2----E_2---F_2$

Due to symmetry,

$\Rightarrow F_1{E}_2=E_1{F}_2=13cm$

Also, $m_1,m_2$ must be midpoint of $F_1{E}_2$ and $E_1{F}_2$ respectively.

So, $E_1{m}_2=m_1{E}_2=\frac{13}{2}=6.5$

$E_1{m}_2=6.5$

$\Rightarrow E_{1}C+C{m}_2=6.5$

$4+C{m}_2=6,5$

$C{m}_2=2.5$

similarly $m_{1}C=2.5$

$\Rightarrow m_1{m}_2=m_1{C}_1{C}_2=5cm=$ mirror width.

Hence, the answer is $5cm.$