Question

Principal axis of a thin lens is the x-axis. The coordinates of a point object and its image are (-20 cm, 2 cm) and ( 25 cm, -1 cm). Lens is located at:

• A. x = +10 cm
• B. x = -2.5 cm
• C. x = 2 cm
• D. x = -3 cm

Answer 1

The correct option is A x = +10 cm

$\begin{array}{c}\text{Principal axis of lens is}x\text{-axis}\\ \text{so}{h}_0=2cm\\ h_i=-1cm\begin{array}{c}0(-20cm,2cm)\\ I(25cm,-1cm)\end{array}\end{array}$

Distance' between object and image $=20+25=45$

$\begin{array}{c}u+v=45\\ 2v+v=45\\ v=15cm\\ u=2\left(15\right)=30cm\end{array}$

$\begin{array}{c}\text{Distance from}x=+10cm\text{to}x=-20cm\\ \text{is}30cm\text{which is object distance.}\\ \text{is}Distance\text{from}x=+10cm\text{to}x=25cm\\ \text{is}25-10=15cm\text{which is image.}\\ \text{distance.}\end{array}$

$\text{so option}A\text{is correct.}$