## Focal Lengths of Lenses of Refracting Telescope of Given Length and Magnification

The magnification is given by

\[M=\frac{f_{PRIMARY}}{f_{SECONDARY}}\]

For a telescope of length

\[l\]

in normal adjustment, \[f_{PRIMARY}+f_{SECONDARY}=l\]

Suppose

\[m=50, \: l=M\]

, then \[50=\frac{f_{PRIMARY}}{f_{SECONDARY}}\]

and \[f_{PRIMARY}+f_{SECONDARY}=1m\]

From the first of these equations

\[f_{PRIMARY}=50 f_{SECONDARY}\]

and substituting this into the second gives \[50 f_{SECONDARY}+f_{SECONDARY}= 1 \rightarrow f_{SECONDARY}=1/51 \simeq 0.0196 m\]

then \[f_{PRIMARY}=50 f_{SECONDARY} \simeq 50 \times 0.0196 =0.98 m\]