Question

The position of the image formed by the combination of lenses is :  

(1) 30 cm (right of third lens) 

(2) 15 cm (left of second lens) 

(3) 30 cm (left of third lens) 

(4) 15 cm (right of second lens)  

Answer 1

Correct option is : (1) 30 cm (right of third lens) 

Here we will use lens formula three times, for lens 1

\( \begin{aligned} & \mathrm{u}=-30, \mathrm{f}=10 \end{aligned}\)

\( \begin{aligned} & \frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \end{aligned} \)

\( \begin{aligned} & \frac{1}{\mathrm{v}_1}-\frac{1}{-30}=\frac{1}{10} \Rightarrow \mathrm{v}_1=15 \mathrm{cm} \end{aligned} \)

For \(2^{\text {nd }}\) lens \( \mathrm{u}=10, \mathrm{f}=-10\)   

\( \begin{aligned} & \mathrm{v}_2 \rightarrow \infty \end{aligned} \)

\(\begin{aligned}\ & \mathrm{u}_3 \rightarrow-\infty \\ \end{aligned} \) 

\(\begin{aligned} \mathrm{v}_3 \rightarrow+30 \mathrm{~cm} \end{aligned}\)