The electron microscope
You know that electron microscopes can “see” objects too small to be seen by optical microscopes. We discussed in Chapter 30 of Vol. I the basic limitations of any optical system due to diffraction of the lens opening. If a lens opening subtends the angle $2\theta$ from a source (see Fig. 29–8), two neighboring spots at the source cannot be seen as separate if they are closer than about \begin{equation*} \delta\approx\frac{\lambda}{\sin\theta}, \end{equation*}  where $\lambda$ is the wavelength of the light. With the best optical microscope, $\theta$ approaches the theoretical limit of $90^\circ$, so $\delta$ is about equal to $\lambda$, or approximately $5000$ angstroms. The same limitation would also apply to an electron microscope, but there the wavelength is—for $50$-kilovolt electrons—about $0.05$ angstrom. If one could use a lens opening of near $30^\circ$, it would be possible to see objects only $\tfrac{1}{5}$ of an angstrom apart. Since the atoms in molecules are typically $1$ or $2$ angstroms apart, we could get photographs of molecules. Biology would be easy; we would have a photograph of the DNA structure. What a tremendous thing that would be! Most of present-day research in molecular biology is an attempt to figure out the shapes of complex organic molecules. If we could only see them! Unfortunately, the best resolving power that has been achieved in an electron microscope is more like $20$ angstroms. The reason is that no one has yet designed a lens with a large opening. All lenses have “spherical aberration,” which means that rays at large angles from the axis have a different point of focus than the rays nearer the axis, as shown in Fig. 29–9. By special techniques, optical microscope lenses can be made with a negligible spherical aberration, but no one has yet been able to make an electron lens which avoids spherical aberration.  In fact, one can show that any electrostatic or magnetic lens of the types we have described must have an irreducible amount of spherical aberration. This aberration—together with diffraction—limits the resolving power of electron microscopes to their present value. The limitation we have mentioned does not apply to electric and magnetic fields which are not axially symmetric or which are not constant in time. Perhaps some day someone will think of a new kind of electron lens that will overcome the inherent aberration of the simple electron lens. Then we will be able to photograph atoms directly. Perhaps one day chemical compounds will be analyzed by looking at the positions of the atoms rather than by looking at the color of some precipitate!