AcademyGeometric Optics
Academy
Telescopes
Level 1 - Physics topic page in Geometric Optics.
Principle
A telescope increases angular size of distant objects by comparing objective and eyepiece focal lengths.
Notation
\(f_o\)
objective focal length
\(\mathrm{m}\)
\(f_e\)
eyepiece focal length
\(\mathrm{m}\)
\(M\)
angular magnification
1
\(L\)
tube length
\(\mathrm{m}\)
\(D_o\)
objective diameter
\(\mathrm{m}\)
Method
Derivation 1: Astronomical telescope
For relaxed viewing, the objective forms an image at the eyepiece focal plane.
Angular magnification
\[M=-\frac{f_o}{f_e}\]
Tube length
\[L=f_o+f_e\]
Derivation 2: Galilean telescope
A diverging eyepiece shortens the tube and produces an upright image.
Diverging eyepiece
\[f_e<0\]
Tube length
\[L=f_o+f_e\]
Magnification
\[M=-\frac{f_o}{f_e}\]
Rules
Telescope magnification
\[M=-f_o/f_e\]
Astronomical length
\[L=f_o+f_e\]
Light gathering
\[\text{brightness}\propto D_o^2\]
Examples
Question
An astronomical telescope has
\[f_o=1.20\,\mathrm{m}\]
and \[f_e=2.0\,\mathrm{cm}\]
Find \(M\).Answer
\[M=-\frac{1.20}{0.020}=-60\]
The image is inverted.Checks
- Larger objective focal length increases angular magnification.
- Larger objective diameter improves light gathering and resolution.
- A negative magnification indicates inversion.