Magnification

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Microscope is based on 4-f system which consist of two lenses; an objective lens and a tube lens. By two lens, the magnification is determined

$$ M=\frac{f_{\rm tube}}{f_{\rm obj}} $$

where $f_{\rm obj}$ and $f_{\rm tube}$ are the focal lengths of the objective lens and tube lens respectively.

Resolution

Numerical aperture is the

$$ ({\rm NA}) = n \sin \theta $$

$n$ refractive index of immersion medium

$\theta$ half angle of the light cone

Under the paraxial approximation ($\le 15{^\circ}$)

$$ ({\rm NA}) = \frac{(D/2)}{f} $$

$D$ diameter of the lens

$f$ focal length

$$ w_0 \rightarrow \frac{\lambda}{2({\rm NA})} \\ z_R = \frac{\pi w_0^2}{\lambda} $$