## Microscopes Summary

- The microscope is a multiple-element system having more than a single lens or mirror.
- Many optical devices contain more than a single lens or mirror. These are analysed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray tracing and thin lens techniques apply to each lens element.
- The overall magnification of a multiple-element system is the product of the magnifications of its individual elements. For a two-element system with an objective and an eyepiece, this is
\(m={m}_{\text{o}}{m}_{\text{e}}\text{,}\)

where \({m}_{\text{o}}\) is the magnification of the objective and \({m}_{\text{e}}\) is the magnification of the eyepiece, such as for a microscope.

- Microscopes are instruments for allowing us to see detail we would not be able to see with the unaided eye and consist of a range of components.
- The eyepiece and objective contribute to the magnification. The numerical aperture \((\text{NA})\) of an objective is given by
\(\text{NA}=n\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\alpha \)

where \(n\) is the refractive index and \(\alpha \) the angle of acceptance.

- Immersion techniques are often used to improve the light gathering ability of microscopes. The specimen is illuminated by transmitted, scattered or reflected light though a condenser.
- The \(f\text{/#}\) describes the light gathering ability of a lens. It is given by
\(f\text{/#}=\cfrac{f}{D}\approx \cfrac{1}{2\mathrm{NA}}.\)

## Glossary

### compound microscope

a microscope constructed from two convex lenses, the first serving as the ocular lens(close to the eye) and the second serving as the objective lens

### objective lens

the lens nearest to the object being examined

### eyepiece

the lens or combination of lenses in an optical instrument nearest to the eye of the observer

### numerical aperture

a number or measure that expresses the ability of a lens to resolve fine detail in an object being observed. Derived by mathematical formula

\(\text{NA}=n\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\mathrm{\alpha ,}\)

where *\(n\)* is the refractive index of the medium between the lens and the specimen and \(\alpha =\theta /2\)