Subject: Applied Physics 2

Topic: Motion Of Charged Particles In Electric And Magnetic Fields

Difficulty: Medium

Bethe’s formula for electron refraction is given by

                         sinϴ1/sinϴ2  =√(V2/V1)

It is identical to snells law in optics but the difference is that order of velocities is reversed. When a light enters from rarer to denser medium it slows and bends to the normal but when electron enters from lower to higher potential it is accelerated and is bend towards the normal. This can be extended to any arbitrary nonuniform electric field. Figure below shows equipotential surfaces separating regions of potentials $V_1$, $V_2$, $V_3$, $V_4$ etc.

At each surface electron path bends to the normal. So, electron follows a curved path in a nonuniform field.