PHY
UNIT- 4WAVE OPTICS & ELECTRON BALLISTICS Q1) In a Newton’s rings experiment the diameter of the 15th ring was found to be 0.59 cm and that of the 5th ring is 0.336 cm. If the radius of curvature of the lens is 100 cm, find the wave length of the light.A1)The given data areDiameter of Newton’s 15th ring (D15) = 0.59 cm = 0.59×10–2 mDiameter of Newton’s 5th ring (D5) = 0.336 cm = 0.336 × 10–2 mRadius of curvature of lens (R) = 100 cm = 1 mWave length of light (λ) = ?Here m is difference between rings = 15-5=10 λ = D2n+m - D2n / 4mRλ = (0.59×10–2 )2- (0.336 × 10–2)2 / 4 x 10 x 1 λ = 0.3481 x10-4 – 0.112896 x10-4 / 40 λ =0.00588 x 10-4 m λ =5880 x 10-10 m λ =5880ÅQ2) Discuss Newton’s Ring and also derive the formula for diameter of bright and dark fringes?A 2)Newton’s RingsNewton’s Rings are the circular interference pattern first discovered by physicist Sir Isaac Newton in 1704. It is cosists of concentric bright and dark rings with the point of contact of lens and the glass plate as centre, The fringes obtained by interference of light waves by using the following arrangementWhen a Plano convex lens with large radius of curvature is placed on a plane glass plate such that its curved surface faces the glass plate, a wedge air film (of gradually increasing thickness) is formed between the lens and the glass plate. The thickness of the air film is zero at the point of contact and gradually increases away from the point of contact.
Figure 8: Newton Ring AssemblyIf monochromatic (means light with single wavelength) light is allowed to fall normally on the lens from a source 'S', then two reflected rays R1 (reflected from upper surface of the film) and R2 (reflected from lower surface of the air film) interfere to produce circular interference pattern. This interference pattern has concentric alternate bright and dark rings around the point of contact. This pattern is observed through traveling microscope.Mathematical analysis of Newton’s Ring
Figure 9 : Mathematical analysis of Newton’s Ring(OL)2 =(O’M)2-(ML)2 ……….(1)R2=(R-t)2 +rn2R2=R2 +t2-2Rt +rn2Radius is large as compared to the thickness so t2 is neglected as t2<< R2R2=R2 +-2Rt +rn22Rt =rn2Thickness of the film t =rn2 /2R ……….(2)Theory of Fringes:The effective path difference between the two reflected rays R1 and R2 for a wedge shaped film from equation ∆ = 2μtcos(r+θ) +λ/2 ……….(3)If the light is incident normally on the lens, r = 0 and near to point of contact θ is small; Therefore near point of contact, (r+θ) approaches to 0 and cos(r+θ)=cos0=1Therefore∆ = 2μt+λ/2 ……….(4)Also At point of contact t = 0 therefore the effective path difference ∆ = λ/2Which is odd multiple of λ/2 Therefore the Central fringe is dark.Bright Fringe : Condition of Maxima For the condition of maxima the effective path difference∆ = ±nλUsing equation (4) ∆ = 2μt+λ/2 we have 2μt+λ/2= ±nλ2μt = ± (2n-1)λ /2 ……….(5)Diameter of Bright Ringswe know by equation (2) t =rn2 /2R substitute in equation (5) we have2μ (rn2 /2R) = ± (2n-1)λ /2rn2 = ± (2n-1)λR /2μ We know diameter D=2r and for nth fringe Dn=2rnso we have Dn2=± 2(2n-1)λR /μ Dn=
The medium enclosed between the lens and glass plate is if air therefore, 
=1. The diameter of nth order bright fringe will beD=
n=0,1,2,3,4……. ……….(6)The diameter of bright ring is proportional to square root of odd natural numbersDark Fringe : Condition for Minima For the condition of minima, The effective path difference∆ =± (2n+1)λ /2 2μt+λ/2 =± (2n+1)λ /22μt= ±nλ ……….(7)it is clear that for particular dark or bright fringe t should be constant.Every fringe is the locus of points having equal thickness. Hence the fringes are circular in shape.Diameter of Dark Rings we know by equation (2) t =rn2 /2R substitute in equation (7) we have2μ (rn2 /2R ) = nλrn2 = nλR/ μWe know diameter D=2r and for nth fringe Dn=2rnso we have Dn2= 4nλR/ μDn= 
The medium enclosed between the lens and glass plate is if air therefore, 
=1. The diameter of nth order bright fringe will beDn= 
n=0,1,2,3,4……. ……….(8)The diameter of dark ring is proportional to square root of natural numbersQ3) Newton’s rings are observed in the reflected light of wave length 5900 Å. The diameter of 10th dark ring is 0.5 cm. Find the radius of curvature of the lens used.A 3)The given data areWave length of light (λ) = 5900 Å= 5900 × 10–10 mDiameter of 10th Newton’s dark ring (D10) = 0.5 cm = 0.5 × 10–2 mRadius of curvature of lens (R) = ?Formula is D2n = 4nλRR= D2n /4nλ R= (0.5 × 10–2)2 /4x 10 x 5900 × 10–10 R= 0.25 x10-4 /236x10-7R=1.059m Q4) Show that the fringe width of newton’s rings reduces with increase in n. orShow that the spacing of newton’s rings gets closer with increase in n.A 4)Spacing between FringesThe Newton’s rings are not equally spaced because the diameter of ring does not increase in the same proportion as the order of ring and rings get closer and closer as ‘n’ increases.For example the diameter of dark ring is given by Dn= 
where n=0,1,2,3,4……. D3 - D2 =
- 
= (
-
)
= 0.635
D7 – D6 =
- 
= (
-
)
= 0.392
D10– D9 =
- 
= (
-
)
= 0.324
From above result we conclude that the fringe width reduces with increase in n. Q5 ) What happens when we use white light in newton’s rings method instead of monochromatic light? A5)Newton’s Ring with White LightIf the monochromatic source is replaced by the white light, dark and bright fringes are not produced. Because the diameter of the rings depends upon wavelength and it is proportional to the square root of wavelength.If If the monochromatic source is replaced by the white light superposition of rings take place due to different wavelength. Few coloured rings are seen around dark centre later illumination is seen in the field of view. As shown in below figure.
Figure 10: Newton’s ring with white lightQ6) What do you mean by interference?A 6)Interference in light waves occurs whenever two or more waves overlap at a given point.TYPES OF INTERFERENCEInterference of light waves can be either constructive interference or destructive interference.Constructive Interference: Constructive interference takes place when the crest of one wave falls on the crest of another wave such that the amplitude is maximum. These waves will have the same displacement and are in the same phase.Destructive Interference: In destructive interference the crest of one wave falls on the trough of another wave such that the amplitude is minimum. The displacement and phase of these waves are not the same.
We know that the superposition of two mechanical waves can be constructive or destructive. In constructive interference, the amplitude of the resultant wave at a given position or time is greater than that of either individual wave, whereas in destructive interference, the resultant amplitude is less than that of either individual wave. Light waves also interfere with each other. Fundamentally, all interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine. If two light bulbs are placed side by side, no interference effects are observed because the light waves from one bulb are emitted independently of those from the other bulb. The emissions from the two light bulbs do not maintain a constant phase relationship with each other over time. Light waves from an ordinary source such as a light bulb undergo random phase changes in time intervals less than a nanosecond. Therefore, the conditions for constructive interference, destructive interference, or some intermediate state are maintained only for such short time intervals. Because the eye cannot follow such rapid changes, no interference effects are observed. Such light sources are said to be incoherent. Q7) What are the conditions to obtain sustained interference of light?A 7)In a sustained interference pattern, the position of maximum and minimum intensity regions remains constant with time. To obtain the sustained interference, the following conditions are required:The sources must be coherent, that is, they must maintain a constant phase with respect to each other. The two light sources must emit continuous waves of the same wavelength and having the same time period.The distance between the two sources of light must be small. This gives large fringe width so that the fringes are separately visible. The sources should be monochromatic, that is, of a single wavelength.The two light sources must emit waves in nearly the same direction. Light source must be a point source. The distance between the two sources and screen must be large. This gives again large fringe width so that the fringes are separately visible. Q8) Discuss the interference in uniform thin film ?A 8)Consider a thin film of uniform thickness ‘t’ and refractive index μ bounded between air. Let us consider monochromatic ray AB is made incident on the film, at B part of ray is reflected (R1) and a part is refracted along BC. At C The beam BC again suffer partial reflection and partial refraction; the reflected beam CD moves again suffer partial reflection and partial refraction at D. The refracted beam R2 moves in air. These two reflected rays R1 and R2 interfere to produce interference pattern.
Figure 6: Interference due to thin films of uniformThe optical path difference between the two reflected rays 
In ΔBDN, sin i = BN / BD and BC = CD as ΔBMC ≡ ΔMCD, therefore
In ΔBMC, cos r = t /BC, therefore
In ΔBMC, tan r = BM / t , therefore
According to snell’s law
................ (1)Correction on account of phase change at reflection: When a beam is reflected from a denser medium (ray R1 at B), a path change of λ/2 occur for the ray. 
….............. (2)Therefore the true path difference isCondition of Maxima (Bright Fringe) Maxima occur when path difference 
............... (3)Condition for Minima (Dark Fringe)Minima occur when path difference 
................. (4)INTERFERENCE IN THIN FILM (TRANSMITTED RAYS)The optical path difference between transmitted rays T1 and T2 will be This path difference is calculated in the same way as above to get
................. (5)Condition of Maxima (Bright Fringe) Maxima occur when path difference, 
................... (6)Condition for Minima (Dark Fringe)Minima occur when path difference, 
............. (7)Q9) Discuss the Principle, construction, and working of Bainbridge Mass Spectrograph?A 9)Bainbridge mass spectrometer is an instrument used for the accurate determination of atomic masses. PRINCIPLEUniform magnetic field acting normal to the path of ions having the same velocity deflects the ions of different masses from a straight path to a circular path of different radii. CONSTRUCTION(i) Ionization ChamberThe ionization chamber is used to ionize the gas whose mass or isotope is to be determined and positive ions are produced. (ii) Velocity SelectorVelocity selector has two fields electric and magnetic field both are applied perpendicular to the moving ion beam. A potential (V) is applied between two electrodes to produce the electric field. A magnetic field (strength B) is applied at right angles to the electrostatic field and so the electrostatic and electromagnetic forces act in opposite directions to each other. A velocity selector is used to produce a mono-velocity ion beam and a transverse magnetic field is employed to discriminate between ions of different masses. (iii) Vacuum / Analyzing ChamberVacuum / Analyzing Chamber is a semi-spherical cavity in which another magnetic field B’ is applied perpendicular to the moving positive ion.
Figure 28: Bainbridge Mass SpectrographWORKINGAtoms with one or more electrons removed have a net positive charge and they become positive ions. A beam of positive ions produced in a discharge tube is collimated into a fine beam by two narrow slits S1and S2. This fine beam enters into a velocity selector. The velocity selector allows the ions of a particular velocity to come out of it, by the combined action of an electric and a magnetic field. The velocity selector consists of two plane-parallel plates P1 and P2, which produces a uniform electric field E and an electromagnet, to produce uniform magnetic field B (represented by the dotted circle). These two fields are at right angles to each other and to the direction of the beam. The electric field and magnetic field are so adjusted that the deflection produced by one field is nullified by the other so that the ions do not suffer any deflection within the velocity selector. Ions are formed in the ionization chamber and pass through the cathode, then through collimating slits S1 and S2. The beam is then passed through a velocity selector in which electric and magnetic fields are applied perpendicular to each other. The ion moves in a straight-line path for which both the forces acting on it are equalLet E and B be the electric field intensity and magnetic induction respectively and q be the charge of the positive ion. The force exerted by the electric field is equal to qE and the force exerted by the magnetic field is equal to qvB where v is the velocity of the positive ion. qE =qvBThe velocity of ion which passes undeflected through the velocity selector is v = E/BIn the vacuum chamber, the ions are affected by the magnetic field (B’) alone and so move in circular paths, the lighter ions having the larger path radius. If the mass of an ion is M, its charge q, and its velocity v thenqvB’ =Mv2 /RR =Mv/qB’So the radius of the path is directly proportional to the mass of the ion i. e. R ∝ MFurther substitute the value of vR =ME/qBB’ or M =RqBB’/EIons with different masses trace semi-circular paths of different radii and produce dark lines on the plate. The distance between the opening of the chamber and the position of the dark line gives the diameter 2R from which radius R can be calculated.
Since, B, B′, E, and R are known, the mass of the positive ions and hence isotopic masses can be calculated.Q10) What is CRO? Draw the block diagram of CRO?A 10) (CRO) Cathode Ray OscilloscopeCathode Ray Oscilloscope is a very important electronic measuring instrument that is used to display and measure electrical signals, time intervals, and phase shift between two electrical signals. Non-electrical quantities such as pressure, strain, and temperature can be measured by first converting them into an equivalent voltage using an appropriate transducer. Any CRO consists of the following seven major sectionsCathode Ray Tube (CRT) Timebase circuits Trigger circuits Vertical Circuits Horizontal Circuits High Voltage Power Supply Low Voltage Power Supply The arrangement of these sections in a CRO is shown in fig in the form of a Block diagram.
Figure 19: Block diagram of CROQ11) Discuss Trigger Circuit?A 11) TRIGGER CIRCUIT To display a stationary wave pattern on the CRO screen, the horizontal deflection should start at the same point of the input signal in each sweep cycle. When it occurs it is said that the horizontal sweep voltage is synchronized with the input signal. If the sweep and signal voltages are not synchronized a standstill pattern is not displayed on the screen; the wave pattern moves continuously to the right or left of the screen. Thus synchronization is the method of locking the frequency of the time base generator to the frequency of the input signal so that a stationary display of wave pattern is seen on the CRO screen. The signal will be properly synchronized only when its frequency equals the sweep frequency or submultiple of sweep frequency. That isfsignal = n fsweep
= 
= 
As an example, if the sweep frequency is 50Hz and the signal frequency is 50Hz, one wave is displayed on the screen. On the other hand, if the sweep frequency is 50Hz and the signal frequency is 100Hz, the period of sweep voltage is 20ms, and the period of the signal is 10ms. In the sweep time which is horizontal trace length, the signal goes through two complete cycles. As a result, the two cycles of the signal voltage are displayed on the screen.
Figure 23: Synchronization of sweep and signal voltagesOne of the methods of achieving synchronization is the use of a trigger circuit. The trigger circuit initiates the time base so that the horizontal deflection sweeps in synchronization with the vertical signal. For this, a delay line circuit is used which delays the signal before it reaches y-deflecting plates. A part of the output obtained from the vertical amplifier is fed to the trigger generator. The trigger generator is sensitive to the level of the voltage applied at its input. The circuit monitors the input signal and detects the point when it reaches the selected level while moving towards the selected polarity. When the predetermined level is reached the circuit produces a trigger pulse. This trigger pulse is fed to the time base generator and it acts as a command signal to the time base generator and starts one sweep cycle of the time base. The sweep voltage is not developed in the trigger mode if the input signal is not given. A portion of the trigger pulse is fed to a second circuit, which produces an unblanking bias voltage to bring the grid of CRT to a potential, which allows the electron beam to appear. Thus a stationary display of the wave is seen only above a predetermined level of the input voltage. It happens in each cycle. Because the signal voltage is initiating the sweep cycle, both voltages will be synchronized. By proper adjustment of controls, the trigger pulse may be made to originate when the input signal is going positive or negative or at any particular voltage level. However, in AUTO trigger mode the trigger circuit will automatically provide a trigger pulse to the sweep generator even when the input signal is not applied to it and the horizontal trace is seen even without signal at Y-input. Q12) What do you mean by delay line?A 12)All electronic circuitry in the CRO causes a certain amount of time delay in the transmission of signal voltages to the deflection plates. Comparing the vertical and horizontal circuits in the CRO block diagram, we obtain that a portion of the output signal applied to the vertical CRT plates triggers the horizontal signal. Signal processing in the horizontal circuit consists of generating a trigger pulse that starts the time base generator (sweep generator) then the output of this is given to the horizontal amplifier and then to the horizontal plates. This whole process takes time. The signal of the vertical CRT plates must therefore be delayed by the same amount of time to reach the signal at the same instant as that of a horizontal one. This is the function of the delay line. Q13) Discuss construction and working of Cathode Ray Tube (CRT)?A13) A Cathode Ray Tube (CRT) is a specially constructed vacuum tube in which an electron beam controlled by electric or magnetic fields generates a visual display of input electrical signals on a fluorescent screen. ConstructionIt consists of three important parts, Electron GunDeflection SystemFluorescent Screen
Figure 16: CRT (Cathode Ray Tube)The CRT resembles a horizontally placed conical flask sealed at its open end. The electron gun consisting of several electrodes is mounted at one end of the tube as a single unit and electrical connections are given to them through base pins. The deflection system consists of two pairs of parallel metal plates mounted in the neck of the tube. They are oriented in such a way that they are in mutually perpendicular directions to the axis of the CRT. The screen consists of a thin coating of phosphors deposited on the inner face of the wide end of the glass envelope. The inner surface of the flare of the envelope is coated with conductive graphite called acquadag. A power supply provides the required potentials to the various elements of CRT. WorkingIn the CRT, the electron gun generates an electron beam, focuses it, and accelerates it towards a fluorescent screen located at the further end of the tube. The electron beam may be moved to any spot on the screen with the help of a deflection system. I) Electron Gun: The indirectly heated cathode K emits a stream of electrons from its coated front face. The electrons pass through the control grid G held at a negative potential. The effective size of the aperture in the grid varies depending upon the potential difference between grid and cathode. The intensity of the glow produced at the screen is determined by the number of electrons striking the screen. Therefore, by varying the negative dc voltage on the grid, the intensity of the luminous spot on the screen is controlled. The grid bias is usually varied between 0 to -50V. The anodes A1 and A3 are internally connected and held at a higher positive potential of a few kilovolts and A2 is maintained at a relatively low positive potential. The anode A1 accelerates the incoming electrons. The Grid G and anode A1 forms the first lens system which prefocusses the electron beam. The anode A2 and A3 constitute the second lens system which focuses the electron beam to a fine point on the fluorescent screen. The focus of the beam is adjusted by varying the positive potential on A2. The anode A3 imparts further acceleration to the electrons as they emerge out of the electron gun. II) Deflection System: There are two types of deflection system namely electrostatic type and electromagnetic type. In the electrostatic deflection system, two pairs of metal plates are employed for deflecting the electron beam. The two plates in each pair are aligned strictly parallel to each other as shown in the figure and the two pairs of plates are mounted at right angles to each other and also at right angles to the path of electrons. One pair of plates is arranged horizontally. When a potential difference is applied to the plates then the uniform electric field is produced in the vertical direction. The fields act perpendicular to the beam and deflect the beam vertically, so these are called vertical deflecting plates or Y-plates. The second set of plates is oriented vertically and produces the uniform horizontal field when a potential difference is applied between them. The field acts normal to the beam and deflects the beam horizontally so this set of plates is called horizontal deflection plates or X-plates.
Figure 17: Electron beam deflection (a) Vertical deflection (b) Horizontal DeflectionWhen voltages are not applied to X-plates and Y-plates, the electron beam travels along the CRT axis and strikes the geometrical centre of the viewing screen. When a dc voltage is applied to Y-plates, the electron beam gets deflected vertically and when a dc voltage is applied to the X-plates, the electron beam is deflected horizontally as shown in figures. The amount of deflection depends on the magnitude of the applied voltage. When dc voltages are applied to both the X and Y plates, the electron beam will be acted upon simultaneously by two forces due to vertical and horizontal electric fields and gets deflected along the direction of their resultant is shown in fig. Thus by varying the dc voltages of the vertical and horizontal planes, the luminous spot may be moved to any position in the plane of the screen.
Figure 18 (a) Voltage not applied to deflection plates (b) Positive voltage applied to UVDP III) Fluorescent Screen: The interior surface of the circular front face of the CRT is coated with a thin translucent layer of phosphors. The phosphor coating glows at the point where it is struck by the high energy electron beam. At that spot, the coating continues to glow for a short period even after the electron beam moves away. So electron beam position can be located with the help of a fluorescent screen. Aquadag CoatingElectrons impinging on the screen tend to charge it negatively and repel the electrons arriving afterward it will reduce the number of electrons reaching the screen leading to a decrease in the brightness of the glow. Therefore, the electrons are to be conducted away. Similarly, the cathode assumes gradually a positive charge as electrons are emitted from it in large numbers. It again leads to a reduction in the intensity of the glow on the screen. Therefore, the cathode is to be replenished with electrons. This is accomplished by the Aquadag coating. The inner surface of the flare of the glass envelope of CRT is coated with conductive graphite coating called Aquadag. It is used to complete the circuit from screen to cathode. The electrons striking the fluorescent screen not only causes the emission of light but also produce secondary emission of electrons. The secondary electrons are attracted by the Aquadag coating which is electrically connected to anode A3. The electrons are restricted to the cathode through the ground. The electrostatic CRT is used in CRO as a display device and study of waveforms. Q14) Write down the uses of CRO?A 14)USE OF CRO (CATHODE RAY OSCILLOSCOPE)The CRO is a versatile electronic instrument and it is used in measuring a variety of electrical parameters. a) Study of the WaveForms: CRO is widely used in maintenance and troubleshooting where the wave shapes of voltages in different electronic circuits are to be examined. The signal under study is applied at the Y-input terminal and the sweep voltage is internally applied to X-plates. The size of the figure displayed on the screen may be adjusted suitably by adjusting the gain control. b) Measurement of D. C. Voltages: The D. C. voltage understudy is applied at Y-input. The trace gets deflected upward or downward depending upon the polarity of the applied voltage. The deflection of the spot produces on the screen can be measured and by multiplying it with the deflection sensitivity (volts/div), the magnitude of unknown voltage can be obtained. c) Measurement of A. C. Voltages: For this measurement, the trace is to be adjusted at the center of the screen, and the A. C. voltage understudy is applied at Y-input. The peak to peak distance is measured and by multiplying it with deflection sensitivity (volts/div), peak to the peak value of applied A. C. voltage can be calculated. The rms value and average value of the voltage are calculated using the formulae, VP = 
Vrms 
Vaver = 0. 636 
d) Measurement of Current: We can measure the value of current or magnitude and direction of current using CRO. By calculating the amplitude variation, horizontal and vertical cells in the CRO screen we can measure the current. We can measure both AC and DC in CRO. For this measurement, the current has to be passed through the suitable known resistor and the potential developed across it can be measured as has been explained above. The current may then be calculated. However, if the cathode ray oscilloscope having a magnetic deflection system, the currents may be measured by passing it through one of the deflection coils. e) Measurement of Frequency: We not only measure voltage and current using CRO, but we can also measure the frequency of a signal by calculating the period. Once we measure the period of a signal then we can easily measure the frequency. The measurement of the period using CRO also very easy. 1) Calibration Method: A sinusoidal signal whose frequency is to be determined is applied to Y-input. The time base control is adjusted to obtain 2 or 3 cycles of the signal on the screen. The horizontal spread of one cycle is noted. By multiplying it with the time base sensitivity (time/div), the period of the signal is obtained. The reciprocal of the period gives the frequency of the signal. 2) Lissajous Method: Alternatively, the frequency of a test signal can be determined using Lissajous patterns. When two sine waves oscillating in mutually perpendicular planes are combined, different types of closed-loop patterns are obtained. They are called Lissajous patterns in honour of the French physicist Lissajous. The signal of unknown frequency is applied to vertical input (Y) and a voltage of known frequency obtained from the standard variable frequency generator is given to horizontal input (X). The frequency of this frequency generator can be varied until a suitable stationary Lissajous figure is obtained. Knowing the frequency from the frequency generator and counting the number of tangency points along horizontal and vertical axes, the unknown frequency can be determined. If fY and fX are the unknown and known frequencies of the sinusoidal voltage fed to the vertical and horizontal plates of CRO respectively and nx and ny are the number of tangency points along the X and Y-axis respectively then the unknown frequency is calculated from
………(1)Where fx is the known frequency. Examples of measurements are:
Figure 25: Measurement of Frequencyf) Measurement of phase difference: Most of the CROs have two channels. We can apply two different signals at a time on the CRO. And we can measure easily the phase difference between the two different signals. Lissajous figures in the CRO screen help us to measure the phase difference between two signals. Using this method, we can also measure the frequency of two signals at a time. (i) Dual Sweep Method: It requires a dual trace CRO. The phase relationship between two sinusoidal signals of the same frequency may be directly measured by displaying both waveforms on the CRO screen and determining the delay time between the two waveforms.
Figure 26: Measurement of phase differenceThe sensitivity and trigger controls of each channel are adjusted for two stationary sinusoidal signals. The sweep speed is initially adjusted such that the period T of the sine wave is measured. Then the sweep speed is increased and the delay time Td between the two sine waves is accurately determined. The difference is calculated using the relation = 
(ii) Lissajous Pattern Method: A second method for determining the phase difference of two sine waves of the same frequency is to feed one sine wave to vertical input and another sine wave to horizontal input. The sweep selector switch is kept in EXT position. A Lissajous pattern namely an ellipse is obtained on the screen. By measuring the lengths A= 2Y1and B=2Y2 of the elliptical = sin-1( 
)Pattern the phase shift is calculated. = sin-1 
Figure 27: Lissajous Pattern MethodQ15) Discuss Time Base Circuit?A 15)TIME BASE CIRCUIT The faithful display of the signal variation by the electron beam requires the beam to move horizontally at a uniform rate across the screen, covering equal distances in equal intervals of time. This condition is satisfied by ramp voltage or saw tooth voltage. The ramp voltage is generated by Time Base Circuit. The time base circuit consists of a time base generator. The time base generator is a variable frequency oscillator that produces an output voltage of sawtooth shape.
Figure 21: Time base voltageTo obtain a visual display of the waveform of applied voltage, it is necessary to apply this A. C. voltage to one set of the deflection plates say Y-plates, and the other time base voltage or ramp voltage, generated by time base generator, to X-plates. This time base voltage is periodic and its frequency can be varied. This voltage increases linearly with time and after reaching a maximum value (Vx)max, it suddenly drops to minimum value (Vx)min. When this voltage is applied to the horizontal deflection plates, the luminous spot sweeps the face of the screen at a uniform velocity from the left edge to the right edge depending on the polarity of the voltage. Because of this reason ramp voltage is also called sweep voltage. The deflection of the spot becomes maximum when the voltage reaches the value (Vx)max after which the spot suddenly returns to its original position. If the frequency of the time base voltage is sufficiently high the trace of the spot appears as a straight line. Due to the resemblance of sweep voltage to teeth of a saw, it is also called saw-tooth voltage. Sweep Time or Trace Time (ts):The time taken by the sweep voltage to rise from its maximum negative voltage to its maximum positive voltage is called sweep time or a trace time tS. Retrace Time or Flyback Time (tr):The time taken by the sweep voltage to dip from its maximum positive voltage to its maximum negative voltage is called retrace time or fly back time tR. Sweep Period (Tsweep): The sum of sweep time and retrace time constitutes the sweep period Tsweep. Tsweep= ts+ tr ≈ tsBlanking: The retrace path, if seen on the screen, gives a bad visual effect. By making the retrace time equal to zero, the retrace path can be eliminated. The trace during the flyback time or retrace time can be made invisible by applying a high negative voltage pulse to the control grid in the electron gun which turns off the electron beam momentarily. The process of making a retrace path invisible is known as Blanking of the trace. Display of the signal shape:As the signal is applied to the Y-plates and time base voltage (sweep voltage) to the X-plates, the electron beam is simultaneously subjected to two forces acting in a perpendicular direction. The deflection of the beam at any instant is determined by the resultant of these two forces. Referring to the below fig it is seen that
Figure 22: Display of signal shape At any instant 1, the input signal (signal voltage) is zero and sweep voltage is (Vx)min, the resultant of the forces due to them acts along the left direction and the beam is deflected to the left extreme. At instant 2, the signal amplitude is positive and the sweep voltage is at a lesser negative value. The beam is deflected left upward in the second quadrant of the screen. At instant 3, both the input and sweep voltages are zero. The resultant force is zero and the beam stays at the centre of the screen. At instant 4, the signal amplitude is negative and the sweep voltage is positive. The beam is deflected to right down in the fourth quadrant of the screen. At instant 5, the signal voltage is zero, and the sweep voltage is (vx)max, the electron beam is deflected toward the right extreme along the horizontal direction. Then the beam returns to position 1 and the process repeats. By joining the resultant positions of the spot, it is seen that waveform of the input voltage is faithfully displayed.
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The medium enclosed between the lens and glass plate is if air therefore, =1. The diameter of nth order bright fringe will beD= n=0,1,2,3,4……. ……….(6)The diameter of bright ring is proportional to square root of odd natural numbersDark Fringe : Condition for Minima For the condition of minima, The effective path difference∆ =± (2n+1)λ /2 2μt+λ/2 =± (2n+1)λ /22μt= ±nλ ……….(7)it is clear that for particular dark or bright fringe t should be constant.Every fringe is the locus of points having equal thickness. Hence the fringes are circular in shape.Diameter of Dark Rings we know by equation (2) t =rn2 /2R substitute in equation (7) we have2μ (rn2 /2R ) = nλrn2 = nλR/ μWe know diameter D=2r and for nth fringe Dn=2rnso we have Dn2= 4nλR/ μDn= The medium enclosed between the lens and glass plate is if air therefore, =1. The diameter of nth order bright fringe will beDn= n=0,1,2,3,4……. ……….(8)The diameter of dark ring is proportional to square root of natural numbersQ3) Newton’s rings are observed in the reflected light of wave length 5900 Å. The diameter of 10th dark ring is 0.5 cm. Find the radius of curvature of the lens used.A 3)The given data areWave length of light (λ) = 5900 Å= 5900 × 10–10 mDiameter of 10th Newton’s dark ring (D10) = 0.5 cm = 0.5 × 10–2 mRadius of curvature of lens (R) = ?Formula is D2n = 4nλRR= D2n /4nλ R= (0.5 × 10–2)2 /4x 10 x 5900 × 10–10 R= 0.25 x10-4 /236x10-7R=1.059m Q4) Show that the fringe width of newton’s rings reduces with increase in n. orShow that the spacing of newton’s rings gets closer with increase in n.A 4)Spacing between FringesThe Newton’s rings are not equally spaced because the diameter of ring does not increase in the same proportion as the order of ring and rings get closer and closer as ‘n’ increases.For example the diameter of dark ring is given by Dn= where n=0,1,2,3,4……. D3 - D2 = - = ( -) = 0.635 D7 – D6 = - = ( -) = 0.392 D10– D9 = - = ( -) = 0.324 From above result we conclude that the fringe width reduces with increase in n. Q5 ) What happens when we use white light in newton’s rings method instead of monochromatic light? A5)Newton’s Ring with White LightIf the monochromatic source is replaced by the white light, dark and bright fringes are not produced. Because the diameter of the rings depends upon wavelength and it is proportional to the square root of wavelength.If If the monochromatic source is replaced by the white light superposition of rings take place due to different wavelength. Few coloured rings are seen around dark centre later illumination is seen in the field of view. As shown in below figure.
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In ΔBDN, sin i = BN / BD and BC = CD as ΔBMC ≡ ΔMCD, thereforeIn ΔBMC, cos r = t /BC, thereforeIn ΔBMC, tan r = BM / t , thereforeAccording to snell’s law
................ (1)Correction on account of phase change at reflection: When a beam is reflected from a denser medium (ray R1 at B), a path change of λ/2 occur for the ray. ….............. (2)Therefore the true path difference isCondition of Maxima (Bright Fringe) Maxima occur when path difference ............... (3)Condition for Minima (Dark Fringe)Minima occur when path difference ................. (4)INTERFERENCE IN THIN FILM (TRANSMITTED RAYS)The optical path difference between transmitted rays T1 and T2 will be This path difference is calculated in the same way as above to get ................. (5)Condition of Maxima (Bright Fringe) Maxima occur when path difference, ................... (6)Condition for Minima (Dark Fringe)Minima occur when path difference, ............. (7)Q9) Discuss the Principle, construction, and working of Bainbridge Mass Spectrograph?A 9)Bainbridge mass spectrometer is an instrument used for the accurate determination of atomic masses. PRINCIPLEUniform magnetic field acting normal to the path of ions having the same velocity deflects the ions of different masses from a straight path to a circular path of different radii. CONSTRUCTION(i) Ionization ChamberThe ionization chamber is used to ionize the gas whose mass or isotope is to be determined and positive ions are produced. (ii) Velocity SelectorVelocity selector has two fields electric and magnetic field both are applied perpendicular to the moving ion beam. A potential (V) is applied between two electrodes to produce the electric field. A magnetic field (strength B) is applied at right angles to the electrostatic field and so the electrostatic and electromagnetic forces act in opposite directions to each other. A velocity selector is used to produce a mono-velocity ion beam and a transverse magnetic field is employed to discriminate between ions of different masses. (iii) Vacuum / Analyzing ChamberVacuum / Analyzing Chamber is a semi-spherical cavity in which another magnetic field B’ is applied perpendicular to the moving positive ion.
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Since, B, B′, E, and R are known, the mass of the positive ions and hence isotopic masses can be calculated.Q10) What is CRO? Draw the block diagram of CRO?A 10) (CRO) Cathode Ray OscilloscopeCathode Ray Oscilloscope is a very important electronic measuring instrument that is used to display and measure electrical signals, time intervals, and phase shift between two electrical signals. Non-electrical quantities such as pressure, strain, and temperature can be measured by first converting them into an equivalent voltage using an appropriate transducer. Any CRO consists of the following seven major sections
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= = As an example, if the sweep frequency is 50Hz and the signal frequency is 50Hz, one wave is displayed on the screen. On the other hand, if the sweep frequency is 50Hz and the signal frequency is 100Hz, the period of sweep voltage is 20ms, and the period of the signal is 10ms. In the sweep time which is horizontal trace length, the signal goes through two complete cycles. As a result, the two cycles of the signal voltage are displayed on the screen.
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Vrms Vaver = 0. 636 d) Measurement of Current: We can measure the value of current or magnitude and direction of current using CRO. By calculating the amplitude variation, horizontal and vertical cells in the CRO screen we can measure the current. We can measure both AC and DC in CRO. For this measurement, the current has to be passed through the suitable known resistor and the potential developed across it can be measured as has been explained above. The current may then be calculated. However, if the cathode ray oscilloscope having a magnetic deflection system, the currents may be measured by passing it through one of the deflection coils. e) Measurement of Frequency: We not only measure voltage and current using CRO, but we can also measure the frequency of a signal by calculating the period. Once we measure the period of a signal then we can easily measure the frequency. The measurement of the period using CRO also very easy. 1) Calibration Method: A sinusoidal signal whose frequency is to be determined is applied to Y-input. The time base control is adjusted to obtain 2 or 3 cycles of the signal on the screen. The horizontal spread of one cycle is noted. By multiplying it with the time base sensitivity (time/div), the period of the signal is obtained. The reciprocal of the period gives the frequency of the signal. 2) Lissajous Method: Alternatively, the frequency of a test signal can be determined using Lissajous patterns. When two sine waves oscillating in mutually perpendicular planes are combined, different types of closed-loop patterns are obtained. They are called Lissajous patterns in honour of the French physicist Lissajous. The signal of unknown frequency is applied to vertical input (Y) and a voltage of known frequency obtained from the standard variable frequency generator is given to horizontal input (X). The frequency of this frequency generator can be varied until a suitable stationary Lissajous figure is obtained. Knowing the frequency from the frequency generator and counting the number of tangency points along horizontal and vertical axes, the unknown frequency can be determined. If fY and fX are the unknown and known frequencies of the sinusoidal voltage fed to the vertical and horizontal plates of CRO respectively and nx and ny are the number of tangency points along the X and Y-axis respectively then the unknown frequency is calculated from ………(1)Where fx is the known frequency. Examples of measurements are:
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(ii) Lissajous Pattern Method: A second method for determining the phase difference of two sine waves of the same frequency is to feed one sine wave to vertical input and another sine wave to horizontal input. The sweep selector switch is kept in EXT position. A Lissajous pattern namely an ellipse is obtained on the screen. By measuring the lengths A= 2Y1and B=2Y2 of the elliptical = sin-1( )Pattern the phase shift is calculated. = sin-1
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