c
The combination of two lenses \(1\) and \(2\) is as shown in figure.

\(\therefore \quad \frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}\)

According to lens maker's formula

\(\frac{1}{{{f_1}}} = \left( {{\mu _1} - 1} \right)\left( {\frac{1}{\infty } - \frac{1}{{ - R}}} \right)\) \( = \frac{{\left( {{\mu _1} - 1} \right)}}{R}\)

\(\frac{1}{{{f_2}}} = \left( {{\mu _2} - 1} \right)\left( {\frac{1}{{ - R}} - \frac{1}{\infty }} \right)\)

\( = \left( {{\mu _2} - 1} \right)\left( { - \frac{1}{R}} \right)\)   \( =  - \frac{{\left( {{\mu _2} - 1} \right)}}{R}\)

\(\therefore \frac{1}{f} = \frac{{\left( {{\mu _1} - 1} \right)}}{R} - \frac{{\left( {{\mu _2} - 1} \right)}}{R}\)

\(\frac{1}{f} = \frac{{\left( {{\mu _1} - {\mu _2}} \right)}}{R};\)   \(f = \frac{R}{{\left( {{\mu _1} - {\mu _2}} \right)}}\)