Question

Optic axis of a thin equiconvex lens is the $x-axis$. The coordinates of a point object and its image are $(-40,1cm)$ and $(50cm,-2cm)$ respectively. Lens is located at

• A. $x=+20cm$
• B. $x=-30cm$
• C. $x=-10cm$
• D. $origin$

Answer 1

Answer: (C)

$x=-10cm$

$\begin{array}{c}\text{As we can see image is twice of object}\\ m=-\frac{v}{u}=\frac{I}{O}=\frac{-2}{1}=-2\\ \text{Let}|u|=x\text{and |v|=2x}\end{array}$

$\begin{array}{c}|u|+|v|=50-(-40)=90=x+2x\\ x=30cm\end{array}$

$\begin{array}{c}\text{Lens should be placed at a distance of}\\ 30cm\text{in from i.e. at}(-10,0)\text{.}\end{array}$