Question

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

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

Answer 1

The correct option is C $x=-10cm$

$\begin{array}{c}\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \Rightarrow \frac{1}{50}-\frac{1}{\left(-40\right)}=\frac{1}{f}\\ \Rightarrow \frac{1}{50}+\frac{1}{40}=\frac{1}{f}\\ \Rightarrow \frac{1}{200}=\frac{1}{f}\\ \Rightarrow f=\frac{200}{9}cm\\ \frac{x}{2}=\frac{90-x}{1}\\ \Rightarrow x=180-2x\\ \Rightarrow 3x=180\\ \Rightarrow x=60\\ \therefore positionofmirroris-10cm\end{array}$

Hence,

option $\left(C\right)$ is correct answer.