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Find the position of the image formed by the lens combination given in the figure.
Question: Find the position of the image formed by the lens combination given in the figure.

Answer

For \(L_1\) \((\)lens on left\()\)
\(u_1=-30\;\text{cm}\) , \(f_1=10\text{ cm}\)
From lens formula,
\(\frac 1{f_1}=\frac 1{v_1}-\frac 1{u_1}\)  
\(\Rightarrow v_1=15\text{ cm}\)
This will act as virtual object for \(L_2\) .
Now for \(L_2\) ,
\(u_2=10\text{ cm}\)    \(\{\)distance of image by \(L_1\) from \(L_2\}\)
\(f_2=-10\text{ cm}\)
By using lens formula we get,
\(v_2={\infty}\)
This will act as virtual object for \(L_3\) .
Now for \(L_3\) ,
\(f_3=30\text{ cm}\) , \(u_3={\infty}\)
By using lens formula we get,
\(v_3=30\text{ cm}\)
\({\therefore}\)  The position of the image by combination of lens is \(45\text{ cm}\)  from \(L_1\) \( [\)on the right\(]\) or \(30\text{ cm}\)  from \(L_3\)  \([\)on the right\(]\)
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