A convex lens of power $+6$ dioptre is placed in contact with a concave lens of power $-4$ dioptre. What will be the nature and focal length of the combination ?

Power of combination:

${\mathrm{P}}_{\mathrm{c}}={\mathrm{P}}_1+{\mathrm{P}}_2=6-4=2 \mathrm{D}$

$$\begin{gathered} \Rightarrow \frac{1}{{\mathrm{f}}_{\mathrm{c}}(\mathrm{in} \mathrm{m})}=2 \\ \Rightarrow {\mathrm{f}}_{\mathrm{c}}=0.5 \mathrm{m}=50 \mathrm{cm} \end{gathered}$$

since, the power of the combination is positive, the combination will behave as a convex lens.