Question

13. An object is placed $6cm$ in front of a concave mirror having focal length $10cm$. The object height is $1.2cm$. Determine the location and size of image?

Answer 1

Step 1: Note the given data

For concave mirror

Distance between object and mirror, $u=-6cm$

Focal length, $f=-10cm$

Height of object $h_0=1.2cm$

Let $h$be the size of the image and $v$ be the location of the image.

Step 2: Finding the required answers by using the mirror formula and magnification formula

Using the mirror formula

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$$\begin{gathered} \Rightarrow \frac{1}{-10}=\frac{1}{-6}+\frac{1}{v} \\ \Rightarrow \frac{1}{v}=-\frac{1}{10}+\frac{1}{6} \\ \Rightarrow \frac{1}{v}=\frac{-3+5}{30} \\ \Rightarrow \frac{1}{v}=\frac{2}{30} \\ \Rightarrow \frac{1}{v}=\frac{1}{15} \\ \Rightarrow v=15\text{cm} \end{gathered}$$

Using magnification formula

$m=-\frac{v}{u}=\frac{h}{h_0}$

$$\begin{gathered} \Rightarrow \frac{-15}{-6}=\frac{h}{1.2} \\ \Rightarrow \frac{5}{2}=\frac{h}{1.2} \\ \Rightarrow h=\frac{1.2\times 5}{2} \\ \Rightarrow h=\frac{6}{2} \\ \Rightarrow h=3\text{cm} \end{gathered}$$

Hence, the location of the image is $15\text{cm}$ and the size of the image is $3\text{cm}$.