Question

Two identical glass $({\mu }_g=3/2)$ equiconvex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $({\mu }_w=4/3)$. The focal length of the combination is

• A. $f/3$
• B. $f$
• C. $4f/3$
• D. $3f/4$

Answer 1

Answer: (D)

For equiconvex lens
$\frac{1}{A}=\left(\frac{3}{2}-1\right)\left(\frac{1}{R}-\frac{1}{-R}\right)$
$\frac{1}{f}=\frac{1}{2}.\frac{2}{R}$
$R=f$
For $2^{nd}$ lens $\frac{1}{f_2}=\left(\frac{4}{3}-1\right)\left(\frac{1}{-f}-\frac{1}{-f}\right)$
$\frac{1}{f_2}=\frac{1}{3}\times \frac{2}{-f}$
$f_2=\frac{-3f}{2}$
For combination
$\frac{1}{f^{\prime }}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$
$=\frac{1}{f}+\frac{2}{-3f}+\frac{1}{f}$
$\frac{1}{f^{\prime }}=\frac{3-2+3}{3f}=\frac{4}{3f}$
$f^{\prime }=\frac{3f}{4}$