Physics - Geometrical Optics Question with Solution | TestHub

When in contact, the equivalent power of two thin lenses is, $${\mathrm{P}}_1+{\mathrm{P}}_2=10$$ When the lenses are separated by $0.25\mathrm{m}$, ${\mathrm{P}}_1+{\mathrm{P}}_2-0.25{\mathrm{P}}_1{\mathrm{P}}_2=6$ $$\begin{array}{ll}\therefore & 0.25{\mathrm{P}}_1{\mathrm{P}}_2=4\\ \therefore & {\mathrm{P}}_1{\mathrm{P}}_2=16\\ & {\mathrm{P}}_1-{\mathrm{P}}_2=\sqrt{{\left({\mathrm{P}}_1+{\mathrm{P}}_2\right)}^2+4{\mathrm{P}}_1{\mathrm{P}}_2}\\ \therefore & {\mathrm{P}}_1-{\mathrm{P}}_2=\sqrt{36}=\mathrm{6...}(i)\end{array}$$ Adding equations (i) and (ii), we get, $$\begin{array}{rl}{\mathrm{P}}_1& =8\mathrm{D}\\ \therefore {\mathrm{P}}_2& =10-8=2\mathrm{D}\end{array}$$