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BE-II SEMESTER ADVANCED PHYSICS

BE-II SEMESTER ADVANCED PHYSICS. UNIT-III ELECTRON OPTICS DEPARTMENT OF APPLIED PHYSICS. SYLLABUS. Bethe’s Law, Construction & working of Electrostatic lens. CRT. CRO. Applications of C.R.O. Bainbridge mass spectrograph. Cyclotron. Electron Refraction (Bethe’s Law):

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BE-II SEMESTER ADVANCED PHYSICS

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

  2. SYLLABUS • Bethe’s Law, Construction & working of Electrostatic • lens • CRT • CRO • Applications of C.R.O • Bainbridge mass spectrograph • Cyclotron

  3. Electron Refraction (Bethe’s Law): • The bending of electrons by inhomogeneous electric field is called electron refraction. Equi poten tial surface acts as the refracting boundary • The equipotential surface - AB .Potential V1 abruptly changes to V2 Region I V2 > V1 Region II

  4. The normal component of velocity vy undergoes a change whereas the tangential component vx remains constant. • If V2 > V1, v yincreases. • If V2 < V1, vydecreases. • As the tangential velocity component remains constant in region I & region II we havevx = v’x or v1sin θ1 = v2sin θ2.

  5. This is Bethe’s law. • Above fig. demonstrates the motion of an electron in a non uniform electric field represented by equipotential surfaces separating equipotential regions of potentials V1 ,V2 ,V3 ,V4 etc.

  6. Comparison of Bethe’s law with Snell’s law

  7. ELECTROSTATIC LENS Consists of two coaxial short cylindrical metal tubes T1 and T2 of same size held at different potentials V1 and V2 respectively such that V2 > V1.

  8. Comparison between optical lens and electrostatic lens • Light rays are bent only at the two boundaries of a lens but electron beam is refracted continuously through successive equipotential surfaces. • Secondly focal length of glass lens is fixed while focal length of electron lens may be varied by adjusting the potentials V1 and V2 of the tubes.

  9. CATHODE RAY OSCILLOSCOPE (CRO) Block diagram of CRO

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

  11. 1) Cathode ray tube (CRT) Electron Lens Focussing anode Accelerating anode Preaccelerating anode Screen Aquadag coating Aquadag coating A2 Y Y A1 A3 X X G 6.3V A.C. F K Electron beam Electron beam -1350V -1350V +1350 v Astigmatism control Astigmatism control Intensity control Intensity control Focus control Focus control

  12. 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 sawtooth voltage (Vx) max vx 0 tr ts (Vx)min T sweep

  13. Due to its resemblance to the teeth of saw,it is called as sawtooth voltage • 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. • Its frequency is selected with the help of Time/Div control of CRO. This voltage is known as ramp voltage. • 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.

  14. DISPLAY OF SIGNAL VY T/4 V T 0 T/2 Time t Time t 3T/4 VX 0 3T/4 T/4 T/2 T Time t Fig. : Resultant Voltage Waveform • The signal is applied to Y-plate & time base is applied to X-plate. • 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.

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

  16. 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. • It can be achieved by trigger ckt • 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 • Delay line: Delays the signal before it is further amplified & fed to Y-plate.

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

  18. Determination of frequency • 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

  19. 5 VY 1 Y X X 4 6 8 FY 0 2 Time t Y 7 3 FX VX 0 1 2 5 3 4 6 7 8 Time t Fig. : Lissajous Pattern For FY = 2FX Frequency Measurement Using Lissajous Pattern

  20. 1:1 3:1 Frequency Measurement Using Lissajous Pattern

  21. Phase measurement A B • Lissajous pattern method- • One sine wave is fed to vertical input and the other sine wave to the horizontal input. • The phase shift (Φ) is evaluated as-

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

  23. since • They trace lines on the photographic plate called mass spectrum. Thus all these ions traverse a semicircular path of radius R given by Since B and v are constant, Thus if x is the distance of line from S3 then

  24. Linear separation So, mass scale is linear.

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

  26. D shaped dees (electrods) Emerging ion beam Oscillating circuit Magnetic field D1 D2 Cyclicoscillator • Ions will move in a circular path of radius • At each rotation charged particle gains the energy E = 2qV

  27. The time for complete circular path • The frequency of the oscillation is given by • Condition for progressive acceleration • Kinetic energy of the ion emerging from the cyclotron is given as

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

  29. Electrons cannot be accelerated to high energy in cyclotron(Limitations of cyclotron): • As electron is a light particle, its mass increases according to relation: • 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. • Hence, only heavy particles like protons can be accelerated by a cyclotron.

  30. THANK YOU

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