b
\(\text { Here, } \mu_{g}=\frac{3}{2}, \mu_{w}=\frac{4}{3}\)

Focal length \((f)\) of glass convex lens is given by

\(\frac{1}{f}=\left(\mu_{g}-1\right)\left(\frac{2}{R}\right)\)

or \(\frac{1}{f}=\left(\frac{3}{2}-1\right) \frac{2}{R}=\frac{1}{R}\) or \(f=R.........(i)\)

Focal length \((f)\) of water filled concave lens is given by

\(\frac{1}{f^{\prime}} =\left(\mu_{w}-1\right)\left(-\frac{2}{R}\right) \text { or } \frac{1}{f^{\prime}}=\left(\frac{4}{3}-1\right)\left(-\frac{2}{R}\right) \)

\(=-\frac{2}{3 R}=-\frac{2}{3 f} \quad[\text { Using } \operatorname{eqn} .(\mathrm{i})]\)

Equivalent focal length \(\left(f_{e q}\right)\) of lens system \(\frac{1}{f_{e q}}=\frac{1}{f}-\frac{2}{3 f}+\frac{1}{f}=\frac{3-2+3}{3 f}=\frac{4}{3 f}\)

\(\therefore f_{e q}=\frac{3 f}{4}\)