Question

A convex lens of focal length 20cm is combined with a diverging lens of power 6.5D. What is the power and focal length of the combination?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{f}=20\mathrm{cm}=0.2\mathrm{m} \\ \mathrm{P}\text{'}=6.5\mathrm{D} \\ \mathrm{f}\text{'}=\frac{1}{\mathrm{P}\text{'}} \\ \mathrm{f}\text{'}=\frac{1}{6.5} \\ \mathrm{f}\text{'}=0.154\mathrm{m}=15.4\mathrm{cm} \\ \mathrm{Power}\mathrm{of}\mathrm{convex}\mathrm{lens},\mathrm{P}=\frac{1}{\mathrm{f}} \\ \mathrm{P}=\frac{1}{0.2}=5\mathrm{D} \\ \mathrm{The}\mathrm{power}\mathrm{of}\mathrm{combination},{\mathrm{P}}_{\mathrm{C}}=\mathrm{P}-\mathrm{P}\text{'} \\ \left[\mathrm{because}\mathrm{the}\mathrm{power}\mathrm{of}\mathrm{diverging}\mathrm{len}\mathrm{is}\mathrm{negative}\right] \\ {\mathrm{P}}_{\mathrm{C}}=5-6.5=-1.5\mathrm{D} \\ \mathrm{The}\mathrm{focal}\mathrm{length}\mathrm{of}\mathrm{combination},{\mathrm{f}}_{\mathrm{C}}=\frac{1}{{\mathrm{P}}_{\mathrm{C}}} \\ {\mathrm{f}}_{\mathrm{C}}=\frac{1}{-1.5} \\ {\mathrm{f}}_{\mathrm{C}}=-0.667\mathrm{m}=-66.7\mathrm{cm} \end{gathered}$$