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Raj is standing in front of a plane mirror. The distance between Raj and his image is $100\,cm$. If the distance between the mirror and image is $x$. What could be the possible value of $x$ ?

Last updated date: 24th Jul 2024
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Hint:A plane mirror has a flat reflecting surface. Images are of the same size and located behind the mirror. Use the characteristics of an image formed by plane mirror to get to your answer. Plane mirrors form virtual images and are commonly used in homes and other places. We are given distance between the object and his image.

Complete step by step answer:
Distance between the object and mirror is the same as the distance between image and mirror. In plane mirror images are formed behind the mirror and are of the same size as that of the object.The image is formed at an equal distance to that of the object from the mirror.Distance between mirror and image will be half of distance between object and image.

Let’s assume, distance between object and mirror = $u$ and distance between image and mirror=$x$
Here we are given distance between Raj (object) and his image which is equal to $100\,cm$.
Hence $u+x =100\,cm$
And $u=x$.......(Distance between object and mirror is same as that of distance between mirror and image in plane mirrors)
$\therefore x=50\,cm$

Hence, the possible value of $x$ is 50 cm.

Note:Reflection is the bouncing back of light in the same medium .We can directly calculate the value of $x$ just by reminding the distance of object is the same as that of image from mirror in case of plane mirrors. The image produced in the plane mirror is virtual and erect and laterally inverted.