Question

A pencil that is 9cm long is held perpendicular to the surface of a plane mirror with the tip of the pencil lead 12cm from the mirror surface and the end of the eraser 21cm from the mirror surface. What is the length of the image of the pencil that is formed by the mirror? Which end of the image is closer to the mirror surface: the tip of the lead or the end of the eraser?

Short answer

The length of the image of the pencil that is formed is $h\text{'}=9cm$.

The tip of the head is closer to the mirror surface as shown in the diagram.

Step-by-step solution

Calculate the length of the image

Given that the height of the pencil is $h=9cm$and the distance between the tip and the mirror is $s_{tip}=12cm$and between the end of the eraser and mirror is $s_{eraser}=21cm$as shown in the figure below

For the plane mirror, the distance of object$s$ is the same for the image $s\text{'}$.

The ratio between the distance of object and the distance of image is called lateral magnification and is given by

$m=-\frac{s\text{'}}{s}=-1$

The negative sign represents the direction of the image which is behind the mirror. So, the length of the image of the pencil that is formed is $h\text{'}=9cm$.

Calculate the end closer to the mirror surface

The tip of the head has an image formed at the same length 12cm and the image of the end of the eraser is formed at 21cm . So, the tip of the head is closer to the mirror surface as shown in the diagram.