Given: The ratio of dispersive powers, \(\dfrac{{\mathit{\omega }}_{1}}{{\mathit{\omega }}_{2}}=\dfrac{5}{3}\)
Focal length of the concave lens, \({f}_{1}=15cm\)
Using the condition, \(\dfrac{{\omega }_{1}}{{f}_{1}}+\dfrac{{\omega }_{2}}{{f}_{2}}=0\)
\(\dfrac{{\omega }_{1}}{{f}_{1}}=−\dfrac{{\omega }_{2}}{{f}_{2}}\)
\(\dfrac{{\omega }_{1}}{{\omega }_{2}}=−\dfrac{{f}_{1}}{{f}_{2}}\)
\(\dfrac{5}{3}=−\dfrac{-15}{{f}_{2}}\)
\({f}_{2}=9\;cm\)
Positive sign indicates the lens is convex in nature.