31. A convex lens of focal length 80 cm and a concave lens of focal length 50 cm are combined together. What will be their resulting power ?

31. A convex lens of focal length 80 cm and a concave lens of focal length 50 cm are combined together. What will be their resulting power ?

(a) +6.5D

(b) −6.5D

(c) +7.5D

(d) −0.75D

Answer :  (d) −0.75D

\(\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\)

\(=\frac{1}{80}+\frac{1}{-50}\)

\(=\frac{1}{10}\left(\frac{1}{8}-\frac{1}{5}\right)\)

\(P=\frac{1}{f}=\frac{1}{10}\left(\frac{-3}{8\times5}\right)\times\frac{1}{\text{cm}}\)

\(=\frac{-3}{10\times8\times5}\times\frac{1}{10^{-2}\ \text{m}}\)

\(=\frac{-300}{10\times8\times5}=-\frac{3}{4}=-0.75\ \text{D}\)