Question

Two identical glass $(\mu =3/2)$equiconvex lenses of local length f are kept in contact . the space between the two lenses is filles with water $(\mu =4/3)$ the focal length of combination is

• A. $\frac{4f}{3}$
• B. $f$
• C. $\frac{3f}{4}$
• D. $\frac{f}{2}$

Answer 1

The correct option is C $\frac{3f}{4}$

$\begin{array}{c}\text{Given focal length of convex lens}=f\\ \text{So}{f}_1=f_3=\frac{R}{2(\frac{3}{2}-1)}=R=f\\ \text{Now}\\ f_2=\frac{-R}{2(\frac{4}{3}-1)}=\frac{-3}{2}R=-\frac{3}{2}f\end{array}$

$\begin{array}{c}\text{We know that}{P}_{\text{eq}}=P_1+P_2+P_3\\ \frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}\\ \frac{1}{f_{eq}}=\frac{1}{f}-\frac{2}{3f}+\frac{1}{f}\\ f_{eq}=\frac{3f}{4}\end{array}$