Wave Optics:
Wave nature of light, including interference, diffraction, and polarization.
Double-slit experiment and Young's modulus.
Fresnel and Fraunhofer diffraction.
Quantum Mechanics:
Wave-particle duality and the uncertainty principle.
Schrödinger equation and its solutions.
Quantum s...
5.1. INTRODUCTION
Electron optics is a branch of physics which deals with focusing a fine electron beam which scans
the surface of solids in a large number of applications. The study of Electron optics is primarily
based on deflection and focusing of an electron beam by electric and magnetic fields, their
interference while crossing each other and their diffraction or bending when passing through
matter or inside the spacing in its submicroscopic structure. An important role is played here by
various mechanisms which relates electron’s motion with that of projectiles. One should be aware
of how the electron beam will behave in uniform as well as non-uniform electric and magnetic
fields. The foundation of Electron optics is based on the wave properties of electrons, which,
according to quantum theory, can be treated either as particles or as waves. The dual nature of
matter was predicted by De-Broglie in 1924 and then experimentally established by electron
diffraction experiments done by C.J.Davisson, L.H.Germer and G.P.Thomson in 1927.
Beams of electrons exhibit behavior similar to those of light and X rays, and all these are
subjected to the same mathematical descriptions. Motion of electrons in uniform electric field can
be described by simple mathematical equations. This is applicable to large number of electrons
and other charged particles like protons as well. In many practical cases, the field may be non-
uniform. In such non-uniform electric fields, analysis of electron’s motion is very difficult and
creates mathematical difficulties. This problem can be solved by extending the motion of charged
particles in an electrostatic field to Geometrical optics, considering the close resemblance between
the motion of electron in electrostatic field and propagation of light in transparent medium. Light
travels in a straight line in a homogeneous medium and along curved path in inhomogeneous
media. Similarly, electrons travel along straight lines in equipotential region (uniform
electric field), while follows curved path when they pass through points of varying potential
(non-uniform electric field) i.e., electron path deviates as it moves from region of one potential
to the region of another potential. This suggests that motion of electrons in homogeneous and
inhomogeneous electric field can be explained by geometrical optics. This approach was given by
H. Bush, C.J. Davission and C.J. Calbick in 1931.The developments in the field of electron optics
lead to the development of various devices like electron microscope, photomultiplier tubes, Mass
spectrographs and Particle accelerators.
5.2. BASIC CONCEPTS OF MOTION OF CHARGED PARTICLE IN ELECTRIC FIELD
Charge:-
Any particle or an object that establishes an electric field in its surrounding space(area) is said to
have charge on it. Charges are of two types, positive(+ve) and negative(-ve).They are always built
up as collection of elementary charges carried by fundamental particles, protons and electrons.
Charge on a body is always an integral multiple of smallest unit of charge i.e. Q = ± ne,
where n = number of charges & e = charge on particle. When the body is said to be charged, it
contains an excess of electrons or a shortage of electrons.
1
,5.2.1. ELECTRIC FIELD
The region or space around a charged body within which its influence can be felt is called electric
field.
The electric field strength or intensity (E) at a point in space is defined as the amount of force
(F)acting on a unit positive charge (q) placed at that point.
𝐅
𝐄= … … … … … … … (𝟔. 𝟏)
𝐪
Thus, the Electric force (F) acting on unit positive charge (q) is given by
𝑭 = 𝐪𝐄 … … … … … … … (𝟔. 𝟐)
The SI unit for Electric force is Newton.
Also, if a potential difference of V volts is applied Electric field between two parallel plates
separated by distance ‘d’ then Electric field that exists is given by
𝐕
𝐄= … … … … … … … (𝟔. 𝟑)
𝐝
The SI unit for Electric field is Newton/Coulomb (N/C) or Volt/meter(V/m)
5.2.2. ELECTRIC POTENTIAL
Electric potential (V) at a point is defined as the work done(W) on a positive charge(q) tobring it
from infinity to that point.
𝑾
𝑽= … … … … … … … (𝟔. 𝟒)
𝒒
The SI unit for Electric potential is Volts (V) or Joules/Coulomb (J/C).
5.2.3. REPRESENTATION OF ELECTRIC FIELD
Michael Faraday proposed that electric field can be represented and visualized in terms of lines of
force, also called electric field lines.These lines indicate the direction as well as the magnitude of
the field. An arrow on the lines of force indicatesthe direction of the electric field. If it is a
positively charged body, then the electric field lines of force are directed away from the body as
shown in Fig.6.1(a). If the body is negatively charged, then the lines of force are directed towards
the body as shown in Fig.6.1(b).Direction of electric field lines of force is always from potential to
negative potential
2
, Fig.6.1: Representation of electric lines of force from (a) positive charge (b) negative charge (c)
two positively charged bodies (d) two equal and oppositely charged bodies (e) a sheet of positive
charge.
When two positively charged bodies are involved, the electric field lines of force give a vivid
picture of mutual repulsion as shown in Fig.6.1(c). In case of two equal and opposite charges, the
lines of force clearly show mutual attraction, the lines move from positive to negative as shown in
Fig.6.1(d). The lines of force due to an infinitely large positively charged sheet are directed away
from the sheet as shown in Fig.6.1(e). Electric field lines are straight, parallel and equidistant
in uniform electric field, while curved and spaced non-uniformly in non-uniform electric
field.
5.2.5. ELECTRON VOLT
The amount of kinetic energy acquired by electron is very much small compared to a joule and
hence the energy is expressed in electron-volt (eV). This unit is widely used in expressing the
energy of atomic particles.
An electron- volt is defined as the energy acquired by an electron when it gets accelerated through
a potential difference of one volt.
1 eV 1 e 1V 1.602 10 19 CV 1.602 10 19 J
5.3. UNIFORM ELECTRIC FIELD
Electric field is said to be uniform if the intensity (in magnitude) and direction of electric field
is same at every point in that region of space. Such a field can be set up by using two plane
parallel plates of smaller area, separated by smaller distance and insulated from each other.
5.3.1. MOTION OF CHARGED PARTICLE IN UNIFORM LONGITUDINAL ELECTRIC
FIELD
Consider two plane parallel metal plates A and B separated by a distance ‘d’. Let ‘V’ volts be the
potential difference applied between the plates, then the strength of uniform electric field ‘E’ set
up is given as,
𝑉
𝐸= … … … … … … … (6.5)
𝑑
The direction of uniform electric field is from positive plate A to negative plate B as shown in
Fig.6.3.
Fig.6.3: Motion of electron in parallel uniform electric field
Consider an electron of charge ‘e’ & mass ‘m’ be placed at rest and then released in an electric
field.The force experienced by an electron due to the electric field is ,
𝐹 = −𝑒𝐸 … … … … … … … (6.6)
3
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