BEII SEMESTER ADVANCED PHYSICS UNITIII ELECTRON OPTICS DEPARTMENT

BE-II SEMESTER ADVANCED PHYSICS UNIT-III ELECTRON OPTICS DEPARTMENT OF APPLIED PHYSICS

SYLLABUS ØBethe’s Law, Construction & working of Electrostatic lens ØCRT ØCRO ØApplications of C. R. O ØBainbridge mass spectrograph ØCyclotron

Electron Refraction (Bethe’s Law): Ø The bending of electrons by inhomogeneous electric field is called electron refraction. Ø The equipotential surface - AB. Potential V 1 abruptly changes to V 2 Region I V 2 > V 1 Equi poten tial surface acts as the refracting boundary Region II

Ø The normal component of velocity vy undergoes a change whereas the tangential component vx remains constant. Ø If V 2 > V 1, v y increases. Ø If V 2 < V 1, vy decreases. Ø As the tangential velocity component remains constant in region I & region II we have VX = V’X OR V 1 SIN Θ 1 = V 2 SIN Θ 2.

This is Bethe’s law. Ø Above fig. demonstrates the motion of an electron in a non uniform electric field represented by equipotential surfaces separating equipotential regions of potentials V 1 , V 2 , V 3 , V 4 etc.

Comparison of Bethe’s law with Snell’s law Bethe’s Law Snell’s Law When electron ray enters a higher potential region, its velocity increases and bends towards the normal to the surface. When light ray enters a denser medium, velocity decreases and bends towards the normal to the surface. According to Bethe’s Law According to Snell’s Law

ELECTROSTATIC LENS Consists of two coaxial short cylindrical metal tubes T 1 and T 2 of same size held at different potentials V 1 and V 2 respectively such that V 2 > V 1.

Comparison between optical lens and electrostatic lens Ø Light rays are bent only at the two boundaries of a lens but electron beam is refracted continuously through successive equipotential surfaces. Ø Secondly focal length of glass lens is fixed while focal length of electron lens may be varied by adjusting the potentials V 1 and V 2 of the tubes.

CATHODE RAY OSCILLOSCOPE (CRO) Block diagram of CRO

CRO consists of Ø Ø Ø Ø Cathode ray tube (CRT) Time base circuits Trigger circuits Vertical circuits Horizontal circuits Low voltage power supply High voltage power supply

1) Cathode ray tube (CRT) Electron Lens Focussing anode Preaccelerating anode 6. 3 V A. C. G A 1 F A 2 K Accelerating anode A 3 Y Screen Aquadag X coating Electron beam -1350 V Intensity control +1350 v Focus control Astigmatism control

2) TIME BASE CIRCUIT It mainly consist of time base generator. Time base generator is variable frequency generator which produces ramp voltage. Due to its resemblance to the teeth of saw, it is called as saw tooth voltage (Vx) max vx 0 ts (Vx)min T sweep tr

Due to its resemblance to the teeth of saw, it is called as saw tooth voltage Ø X-axis of this voltage not only denotes the amount of horizontal deflection but the time elapsed. Therefore it is called as time base voltage. Ø Its frequency is selected with the help of Time/Div control of CRO. This voltage is known as ramp voltage. Ø The luminous spot sweeps from the left to the right along a straight line in step with the cycle of ramp voltage, therefore also known as sweep voltage.

DISPLAY OF SIGNAL VY 0 T/4 V T T/2 Time t 3 T/4 VX 0 T/4 3 T/4 T/2 T Time t Fig. : Resultant Voltage Waveform Ø The signal is applied to Y-plate & time base is applied to X-plate. Ø The beam deflection at any instant occurs along the direction of resultant of two forces as time progresses, the resultant goes on changing in magnitude & direction.

3) TRIGGER CIRCUIT Tsweep = n Tsignal In general , fsignal = n fsweep t I/p voltage Ts Ts t Sweep +v voltage Tsweep -v Tsweep=2 Ts

Ø Synchronization-is the method of locking the frequency of Time base generator to the frequency of input signal so that a stationary display of wave pattern is seen on CRO screen. Ø It can be achieved by trigger ckt Ø In trigger method, when i/p signal is fed to Y plate it is amplified & fed in two directions 1)Trigger ckt 2)Delay line Ø Delay line: Delays the signal before it is further amplified & fed to Y-plate.

APPLICATIONS Ø Study of the Wave Forms Ø Measurement of D. C. Voltages Ø Measurement of A. C. Voltages Ø Measurement of Current Ø Determination of frequency Ø Phase measurement.

Determination of frequency 1. The simpler method for determining the signal frequency is by measuring its time period and calculating the frequency using the relation: T = t x time base sensitivity Where, t = Horizontal spread of one cycle

5 VY 1 0 4 6 2 8 Time t 7 3 VX 0 5 6 1 3 4 7 2 8 Time t Fig. : Lissajous Pattern For FY = 2 FX Y X X Y FX FY Frequency Measurement Using Lissajous Pattern

1: 1 3: 1 Frequency Measurement Using Lissajous Pattern

Phase measurement Lissajous pattern methodØOne sine wave is fed to vertical input and the other sine wave to the horizontal input. ØThe phase shift (Φ) is evaluated as- A B

Bain Bridge Mass Spectrograph ØThe instrument developed for the purpose of measuring atomic masses of isotopes of an element.

Ø They trace lines on the photographic plate called mass spectrum. Thus all these ions traverse a semicircular path of radius R given by since Since B and v are constant, Thus if x is the distance of line from S 3 then

Linear separation So, mass scale is linear.

CYCLOTRON Ø The devices that impart high energies to the particles are known as particle accelerator. Ø 1. Linear accelerators 2. Cyclic accelerators. Ø The cyclotron is the first cyclic accelerator developed by E. O. Lawrence in 1931.

Oscillating circuit Magnetic field D shaped dees (electrods) D 1 D 2 Cyclic oscillator Emerging ion beam Ø Ions will move in a circular path of radius Ø At each rotation charged particle gains the energy E = 2 q. V

Ø The time for complete circular path Ø The frequency of the oscillation is given by ØCondition for progressive acceleration Ø Kinetic energy of the ion emerging from the cyclotron is given as

Ø If the charged ions undergo N revolutions, the final energy acquired by them is given by E = 2 Nq. V Ø The importance of the cyclotron is that with relatively small voltages high energies can be imparted to the charged particles Function of Electric field: - Ø To impart high kinetic energy to the charge particle. Ø The particles form a sharply focused beam with their orbits essentially confined to a meridian plane. Function of Magnetic field: - Ø To deflect the charged particles along circular path.

Electrons cannot be accelerated to high energy in cyclotron(Limitations of cyclotron): Ø As electron is a light particle, its mass increases according to relation: Ø The time taken by the electron to cover the semicircular path within a dee increases and the particle fails to reach the gap at the moment when the electric field reversal occurs. As a result it gets decelerated. Ø Hence, only heavy particles like protons can be accelerated by a cyclotron.

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