Physics - Geometrical Optics Question with Solution | TestHub

Let's consider the following diagram-

Let's assume that $v_A, v_B$ indicates the distances of the images of objects A and B respectively.

Thus, by mirror formula, for object A, it can be written that

$\begin{array}{rcl}\frac{1}{v}+\frac{1}{u}& =& \frac{1}{f}\\ \frac{1}{v_A}+\frac{1}{-15}& =& \frac{1}{\left(-20\right)}\\ \frac{1}{v_A}& =& \frac{1}{-20}+\frac{1}{15}\\ & =& \frac{-3+4}{60}\\ v_A& =& 60 \mathrm{cm}\end{array}$

Similarly, for object B, using mirror formula,

$\begin{array}{rcl}\frac{1}{v_B}+\frac{1}{\left(-25\right)}& =& \frac{1}{\left(-20\right)}\\ \frac{1}{v_B}& =& \frac{-1}{20}+\frac{1}{25}\\ & =& \frac{-5+4}{100}\\ & =& \frac{-1}{100}\\ v_B& =& -100 cm\end{array}$

Hence, the distance $\left(d\right)$ between the images can be calculated as follows:

$\begin{array}{rcl}d& =& v_A+v_B\\ & =& \left(60+100\right) \mathrm{cm}\\ & =& 160 \mathrm{cm}\end{array}$