Question

a convex lens of focal length 20cm is placed in contact with a concave lens of focal length 10 cm.what is the combination of focal length and power of lens ?

Answer 1

Hi,

Given,
Focal length of convex lens, f₁ = 20 cm
Focal length of concave lens, f₂ = −10 cm
Focal length in combination (F) is given by

$$\begin{gathered} \frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2} \\ \Rightarrow \frac{1}{F}=\frac{1}{20}+\frac{1}{-10} \\ \Rightarrow \frac{1}{F}=\frac{1-2}{20}=\frac{-1}{20} \\ \Rightarrow F=-20\mathrm{cm} \\ \mathrm{Focal}\mathrm{length}\mathrm{of}\mathrm{combination}F\mathrm{is}-20\mathrm{cm}. \\ \mathrm{Power}\mathrm{of}\mathrm{the}\mathrm{lens},P=\frac{100}{F}=-5\mathrm{D} \end{gathered}$$