Question

A candle$\mathbf{4}\mathbf{.}\mathbf{85}\mathbf{}\mathbf{cm}$ tall is$\mathbf{39}\mathbf{.}\mathbf{2}\mathbf{}\mathbf{cm}$ to the left of a plane mirror. Where is the image formed by the mirror, and what is the height of this image?

Short answer

The distance of the image from the candle is $4.85cm$.

Step-by-step solution

Calculate the point where image is formed

Given that $y=4.85cm$and $s=39.2cm$.

In case of plane mirrors, the distance of the image from the mirror is same as distance of the object from the mirror.So, the distance of the image is $39.2cm$.

Calculate the height from magnification

The ratio of the distance of the object to distance of the image is called the lateral magnification. It is given by

$m=-\frac{s\text{'}}{s}=-\frac{39.2}{39.2}=-1$

Also, the lateral magnification is of the form$m=-\frac{y\text{'}}{y}$ , where$y$ is the height of the object and$y\text{'}$ is the height of the image. So,

$$\begin{gathered} \left|y\text{'}\right|=\left|my\right| \\ \left|y\text{'}\right|=\left|-1\times 4.85\right| \\ \left|y\text{'}\right|=4.85cm \end{gathered}$$

So, the distance of the image from the candle is $4.85cm$.