A thin converging lens of focal length $\displaystyle 10$ cm is placed coaxially in contact with a thin diverging lens of focal length $\displaystyle 15$ cm . How will the combination behave? Justify your answer.

It will behave like a converging lens. Power of the converging lens is more than the power of the diverging lens. Hence the combination will behave like a converging lens.$\displaystyle P=P_{1}+P_{2}$ $\displaystyle =\frac{100}{10}+\frac{100}{-15}$ $\displaystyle P=\frac{10}{3} \mathrm{D}$$\displaystyle \frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$ $\displaystyle \frac{1}{f}=\frac{1}{10}-\frac{1}{15}$ $\displaystyle \frac{1}{f}=\frac{1}{30}$ $\displaystyle f=30 \mathrm{~cm}$