Electron Microscope
An electron microscope is in principle similar to that of an optical microscope. In an optical microscope using visible light, focusing is done by suitable lenses whereas in an electron microscope a beam of electrons is used in place of ordinary light and focusing is done by electrostatic and electromagnetic fields.
If a beam of light enters as in interface XY separating two media A and B of refractive indices 
and 
and if i and r are the angles of incidence and refraction.
If v1 and v2 are the velocities of light in the two media, then
According to the wave theory of light
Similarly, an electron beam can be accelerated or retarded by suitable electrostatic and magnetic fields and hence can be refracted as ordinary light waves.
Electrostatic focusing: Let XY be the interface of two regions A and B of uniform electrostatic potentials V1 and V2 (V2 > V1) and v1 and v2 the velocities of the electrons in the regions A and B (very near XY). Here, i and r are the angles of incidence and refraction. If c is the charge of the electrons and m its mass, then for the first medium
Similarly, the velocity of the electron in the second medium is
From (i) and (ii),
Further, if the velocities v1 and v2 are resolved into two components parallel and perpendicular to the surface, then the perpendicular components will be v1 cis i and v2 cos r and the parallel components will be v, sin i and v2 sin r. The component v2 cos r is greater than v1 cos i and hence the electron is accelerated in the direction of the field. If V2 < V1 the electron is retarded. As XY is an equipotential surface there is no change in the component parallel to XY and hence
v1 sin i = v2 sin r
This is similar to Snell’s law of refraction of a ray of light at a surface separating two media.
From (iii) and (iv),
For values of V2 < V1, the beam is deflected towards the normal and for values of V2 < V1, the beam is deflected away from the normal similar to refraction of light.
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