AcademyGeometric Optics
Academy
Microscopes
Level 1 - Physics topic page in Geometric Optics.
Principle
A compound microscope multiplies objective image magnification by eyepiece angular magnification.
Notation
\(f_o\)
objective focal length
\(\mathrm{m}\)
\(f_e\)
eyepiece focal length
\(\mathrm{m}\)
\(L\)
tube length between focal regions
\(\mathrm{m}\)
\(M\)
total angular magnification
1
\(N\)
near point distance
\(\mathrm{m}\)
Method
Derivation 1: Two-stage magnification
The objective forms a real enlarged intermediate image. The eyepiece acts as a magnifier for that image.
Objective magnification
\[m_o\approx-\frac{L}{f_o}\]
Eyepiece magnification
\[M_e\approx\frac{N}{f_e}\]
Total magnification
\[M\approx-\frac{L}{f_o}\frac{N}{f_e}\]
The negative sign indicates image inversion relative to the original object.
Rules
Objective magnification
\[m_o\approx-L/f_o\]
Eyepiece magnification
\[M_e\approx N/f_e\]
Microscope magnification
\[M\approx-\frac{LN}{f_of_e}\]
Examples
Question
A microscope has
\[L=16\,\mathrm{cm}\]
\[f_o=4.0\,\mathrm{mm}\]
and \[f_e=2.5\,\mathrm{cm}\]
Estimate \[|M|\]
Answer
\[|M|\approx\frac{LN}{f_of_e}=\frac{(0.16)(0.25)}{(0.0040)(0.025)}=400\]
Checks
- The objective forms a real intermediate image.
- The eyepiece acts as a magnifier.
- Total magnification is the product of the two stages.