With the help of a ray diagram, show how a compound microscope forms a magnified image of a tiny object, at least distance of distinct vision. Hence derive an expression for the magnification produced by it.

Ray diagram of Compound Microscope Derivation of magnification $\displaystyle 1 \frac{1}{2}$The linear magnification due to objective lens\mathrm{m}_{0}=\frac{h^{\prime}}{h}=\frac{L}{f_{0}} \longrightarrow \cdots \cdots(\mathrm{i})h= size of object h'= size of first image As $\displaystyle \tan \beta=\frac{h}{f_{0}}=\frac{h^{\prime}}{L}$ magnification due to eye piece\mathrm{m}_{\mathrm{e}}=1+\frac{D}{f_{e}} \longrightarrow \ldots \ldots-\ldots-\ldots-\ldots(\mathrm{ii})Total Magnification $\displaystyle \mathrm{m}=\mathrm{m}_{\mathrm{o}} \times \mathrm{m}_{\mathrm{e}}$\mathrm{m} .=\frac{L}{f_{0}}\left(1+\frac{D}{f_{e}}\right) $$