Question

In the figure shown "$O$" represents the point object. Find the coordinates of the image formed by the plane mirror .

• A. $(0,-\sqrt{2})$
• B. $(0,-2)$
• C. $(0,2\sqrt{2})$
• D. $(0,-2\sqrt{2})$

Answer 1

The correct option is D $(0,-2\sqrt{2})$

Extrapolate the mirror to locate the image as shown in the figure.



For a plane mirror ,

Object distance = Image distance

$x=2\sqrt{2}\sin {45}^{\circ }=2\text{units}$

From the given diagram, we can write that,
$y=\sqrt{(2x{)}^2-(2\sqrt{2}{)}^2}$

Substituting the value of $x$, we get

$y=\sqrt{4^2-(2\sqrt{2}{)}^2}=2\sqrt{2}\text{units}$

$\therefore$ Position of image formed on the plane mirror , $I=(0,-2\sqrt{2})$

Hence, option (d) is the correct answer.

$\begin{array}{c}\text{Why this Question}?\\ \text{This question provides understanding of image formation when the mirror is inclined.}\\ \\ \text{Let's try :- For the problem given above , now rotate the mirror and find how the position of image is being changed for a fixed position of object.}\end{array}$