Two identical glass $({\mu }_g=3/2)$ equiconvex lenses of focal length $f$ 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

Water in between the lens can be considered to be a concave lens of refractive index of water as shown in the figure. This suggests that the radius of curvature of all the lenses is same.

Consider the convex lens-

$\frac{1}{f}=\frac{({\mu }_g-1)2}{R}=\frac{(\frac{3}{2}-1)2}{R}$

hence $R=f$

For the concave lens,

$Power=\frac{1}{f_1}=({\mu }_{water}-1)(\frac{-2}{R})=\frac{-2}{3f}$

Power of the lenses get added,

$\frac{1}{f_{combination}}=\frac{1}{f}+\frac{-2}{3f}+\frac{1}{f}$

Hence $f_{combination}=\frac{3f}{4}$