Question

A man $180\text{cm}$ high stands in front of a plane mirror. His eyes are at a height of $170\text{cm}$ from the floor. Then the minimum length of the plane mirror for him to see his full image is

• A. $90\text{cm}$
• B. $180\text{cm}$
• C. $45\text{cm}$
• D. $360\text{cm}$

Answer 1

The correct option is A $90\text{cm}$

Assume that the eyes of the man lies at point O.


$△O{M}_1{M}_2$ & $△O{H}^{\prime }{F}^{\prime }$ are similar triangles

$\Rightarrow \frac{M_1{M}_2}{H^{\prime }{F}^{\prime }}=\frac{l}{2l}$
$\text{Or,}{M}_1{M}_2=\frac{H^{\prime }{F}^{\prime }}{2}$

Therefore minimum length of the mirror should be half of the height of the man

$\therefore M_1{M}_2=\frac{180}{2}=90\text{cm}$

Hence (a) is correct choice.