Question
Prove geometrically that the image formed by a plane mirror is at the same distance behind the mirror as the objects in front of the mirror.

Answer

To understand the reflection from a plane mirror and the image formed due to it, let us consider a point object O kept in front, of the plane mirror strip, MM’.

Image
The rays of light travel out in all directions from O. Consider two light rays OP and OQ from O (point object) and incident on the mirror at points P and Q, respectively. Let these two rays be reflected along PA and QB. Draw the normals PN and QN to the mirror at points P and Q, respectively. As per the laws of reflections, angle of incidence is equal to the angle of reflection for each incident ray and its corresponding reflected ray. Thus,
$\angle i_1=\angle r_1$And $\angle i _2=\angle r _2$
If the reflected rays PA and QB are produced backwards, they meet at a point I, behind the mirror, from where rays seem to be coming and image of the object O is formed. As the reflected rays PA and QB do not actually meet at I but only appear to do so, the image is said to be virtual. Draw a perpendicular from point I to the mirror MM’ to meet MM at S and extend it to meet point O. By measuring the length of OS and SI with a ruler, you will see that OS = SI
i. e., for a plane mirror, the image formed is at the same distance behind the mirror as the object in front of the mirror.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free