Question

A body is $1.8m$ tall and can see his image in plane mirror fixed on a wall. His eyes are $1.6m$ from floor level. The minimum length of the mirror to see his full images is:-

• A. $0.9m$
• B. $0.85m$
• C. $0.8m$
• D. Can't be determined

Answer 1

The correct option is A $0.9m$

From the figure,
$O{O}^{\prime }$ is the boy and point $E$ represents the eyes of the boy.
Incident Ray $OC$ is coming from the head of the boy and after getting reflected, ray $CE$ enters the eye of the boy.
Incident Ray $O^{\prime }D$ is coming from the foot of the boy and after getting reflected, ray $DE$ enters the eye of the boy.
The virtual image of the boy is drawn and is represented by $AB$.

Now,
$CD||AB$
$\therefore \angle ECD=\angle EAB$

and $\angle EDC=\angle EBA$

So by $AA$ similarity postulate
$\Delta ECD\sim \Delta EAB$

$\Rightarrow \frac{CD}{AB}=\frac{EC}{EA}$

We know,

$\frac{EC}{EA}=\frac{1}{2}$
because the distance between image and the object is twice the distance between object and the mirror.

$\Rightarrow \frac{CD}{AB}=\frac{1}{2}$

$\frac{CD}{1.8}=\frac{1}{2}$

$CD=0.9m$

$\therefore$The minimum length of mirror required to see his full image is $0.9m$

Hence, the correct answer is OPTION A.