MEASURING INSTRUMENTS 1. MEASUREMENT OF LENGTH

Transcription

1 MEASURING INSTRUMENTS 1. MEASUREMENT OF LENGTH For the measurement of length usually meter scales are used with an accuracy upto millimeters. To measure length say 1/100 th of a centimeter (or) 1/100 th of a millimeter, it is not possible to measure accurately using meter scale. Hence the following instruments are used for more accuracy. 1. Vernier Calipers (Accuracy upto 1/100 th of cm) 2. Screw gauge (Accuracy upto 1/100 th of mm) 1. VERNIER CALIPERS Design of the Instrument It consists of two scales viz, main scale and vernier scale. The main scale is a long steel bar graduated in inches on the top and in centimeters on the bottom. 10 main scale divisions are equal to 1cm. The vernier scale has 10 divisions which are equal to 9 main scales divisions. There are two metal jaws A & B. A is fixed and B is movable which can be fixed at any position using the screw(s) as shown in figure 1. Fig 1. Vernier Caliper The projections P1 and P2 of the jaws in the upward direction are used to measure the internal diameter of the calorimeter, cylinder, etc. Least Count Least count of vernier calipers is defined as the smallest length that can be accurately measured and is equal to the difference between the main scale division (MSD) and the vernier scale division (VSD). 1

2 Derivation LC = 1 MSD VSD 10 MSD = 1 cm 1 MSD = 1 /10 cm 10 VSD = 9 MSD 1 VSD = 9/10 MSD (or) {9/10} X {1/10} = 9/100 cm LC = {1/10-9/100} cm = 1/100 cm = 0.01 cm No Zero Error To find the zero error of the vernier calipers, the two jaws A and B brought in contact with each other. If the zero of the vernier scale coincides with the zero of the main scale then there is no zero error (Z.E = 0) (fig. 1.1). Hence there is no need to apply zero correction (Z.C = 0). Fig. 1.1 No zero error. Positive Zero Error If the zero of the vernier scale lies on the right side the zero of the main scale, then the instrument has an error called positive zero error (fig. 1.2). This error should be subtracted from the final reading. Thus, the zero correction is negative. Example If the 4 th vernier division coincides with any of the main scale division, then zero error = Vernier Scale coincidence x Least count Fig. 1.2 positive zero error. = VSC x LC = 4 x 0.01 = 0.04 cm Zero Correction = cm Negative Zero Error If the zero of the vernier scale lies on the left side of the zero of main scale, then the instrument is said to have an error called negative zero error (fig. 3). This error should be added to the final reading. Thus, the zero correction is positive. Fig. 1.3 negative zero error. 2

3 Example If the 6 th division of the vernier coincides with any of the main scale division, then Zero Error = - (no. of vernier scale divisions Vernier scale coincidence) x Least count = - (10-6) x 0.01 cm = - 4 x 0.01 = cm Zero Correction = 0.04 cm To find the length of the specimen The specimen whose length (or) outer diameter is to be determined is held between the two jaws. The position of zero of the vernier on the main scale gives the main scale reading (MSR). The vernier division which coincides with any one of the main scale division gives the vernier scale coincidence (VSC), then Observed reading (OR) = MSR+ (VSC X LC) in cms Actual (or) correct Reading = OR ±Zero Correcti0n in cms Example OR = (3 x 0.01) cm CR = 1.23 cm (Zero Error = Nil) 2. SCREW GAUGE Fig 2. Screw gauge 3

4 Design of the Instrument It consists of two scales namely pitch scale and head scale. Pitch scale is a millimeter scale engraved on the cylinder (C), which is rigidly attached with the frame (f). The head scale carrier 100 equal divisions. The specimen can be held in-between the two edges A (fixed) and B (movable) shown in fig. 2. Derivation of Least count LC = Pitch/No. of head scale divisions Pitch = Distance moved on the pitch scale / No. of head scale rotations To find pitch the head is given say, two rotations and the distance moved by the head on the pitch scale is noted Pitch = 2mm/2 = 1 mm Number of head scale division = 100 LC = 1/100 mm LC = 0.01 mm To find zero error To find zero error the stud A and the tip B are kept in contact. If the zero of the head scale coincides with zero of the pitch scale on the reference line, the instrument is said to have no zero error (Fig. 2.1). Fig. 2.1 No zero error. Positive zero error If the zero of the head scale lies below the reference line of the pitch scale, the zero error is positive and the correction is negative (Fig. 2.2). Example If the 2 nd division of the head scale coincides with the reference line of the pitch scale then Zero error = head scale coincidence x Least count = 2 x 0.01 mm = 0.02 mm Zero Correction = mm Fig. 2.2 positive zero error. Negative zero error If the zero of the head scale lies above the reference line of the pitch scale the zero error is negative and the correction is positive (Fig. 2.3). Example If the 96 th division of the head scale coincides with reference line of the pitch scale then, Zero error = - (100 head scale coincidence) x least count = - (100 96) x 0.01 mm = mm Zero correction = 0.04 mm Fig. 2.3 negative zero error. 4

5 To find the diameter of the given wire The wire is gripped gently between the faces A and B. The number of pitch scale divisions just in front of the head scale gives the pitch scale reading. The division on the head scale that coincides with the reference line gives the head scale coincidence. The readings are noted and are tabulated. Example Suppose if the PSR = 5mm H.S.C = 35 div. HSR = HSC x L.C. = 35 x0.01 = 0.35 mm Observed reading = PSR + HSR = = 5.35 mm If the zero error is 0.04 mm (Positive zero error), then the zero correction is 0.04 mm, Correct reading = OR±ZC = ( ) mm = 5.31 mm Design of the Instrument Travelling Microscope consists of an ordinary compound microscope which slides along a graduated vertical pillar, attached to horizontal base resting on the leveling screws. The main scales divisions along with vernier scale divisions are marked on the horizontal base and the vertical pillar as shown in fig.3. The microscope can be moved up and down in the vertical pillar and can be moved in to and fro direction over the horizontal base. Thus the microscope can be moved both in the vertical and horizontal directions. Two fine adjustment screws are provided for the horizontal and vertical movements respectively. The image of the object can be focused by adjusting the side screw (S) attached to the microscope. The eye piece of the microscope is provided with a cross wire. 3. TRAVELLING MICROSCOPE Fig. 3 Travelling Microscope. 5

6 The main scale is divided into millimeter and half a millimeter. Therefore the value of one main scale division (MSD) is 0.5 mm. The vernier scale of the travelling microscope is divided into 50 divisions which are equivalent to 49 main scale divisions. Least count Derivation LC = 1 MSD 1 VSD 20 MSD = 1 cm 1 MSD = 1/20 cm Here 50 VSD = 49 MSD 1 VSD = 49/50 MSD = (49/50) x (1/20) cm 1 VSD = 49/1000 cm LC = (1/20 49/1000) cm = 1/1000 cm LC = cm 4. MEASUREMENT OF ANGLES Fig. 4 Spectrometer. Spectrometer Design of the instrument Spectrometer consists of collimator (c) telescope (T), prism table (p) and vernier table as shown in fig 4. The collimator consists of a convex lens fixed at one end and a slit of adjustable width on the other end. The telescope consists of an objective (O) at one end and an eye piece fixed with the cross wires on the other end. The prism table consists of two circular disc connected by three leveling screws. The vernier tables have two verniers V A and V B each having main scale and vernier scale. 6

7 Here one main scale division is equal to half a degree. Each vernier scale has 30 divisions, which is equal to 29 main scale divisions. Initial adjustments (i) Eye piece adjustment: The eye piece (E) is adjusted until the cross wires are clearly seen when viewed through the telescope. (ii) Distant object method: A clear, well defined inverted and diminished image of a distance object is seen by adjusting the telescope. (iii) Slit adjustment: The slit is made narrow with the help of the screw, provided aside of the slit. (iv) Collimator adjustment: The telescope is brought on line with the collimator. The slit is illuminated by a source of light. If the image of the slit appears blurred, then the screw of the collimator is adjusted until a clear image is seen when viewed through the telescope. Now the rays of light emerging from the collimator will be rendered parallel. (v) Prism table adjustment: The spirit level is placed on the prism table, parallel to the line joining any two leveling screws. The air bubble in the spirit level is brought to the centre by adjusting the two screws. It is then placed in a perpendicular direction and the air bubble is brought at the centre by adjusting the third screw. Now the prism table will be horizontal. (vi) Spectrometer base: The base of the spectrometer is adjusted to the horizontal with the help of the three leveling screws. Least count LC = 1 MSD 1 VSD 1 MSD = ½ degree 30 VSD = 29 MSD 1 VSD = 29/30 MSD 1 VSD = 29/30 x ½ degree 1 VSD = 29/60 degree LC = (1/2-29/60) degree = (30-29)/60 degree = 1/60 degree Since 60 = 1 1 = 1 /60 LC = 1 Measurement Before doing any experiment using spectrometer, the above mentioned initial adjustments have to be made. While performing the experiment, the main scale and vernier scale readings are noted from both the verniers in V A and V B in degree and minutes. 7

8 Fig. 5 Fig.6. Different order of spectrum 8

9 Expt. No.: Date: 1. a. PARTICLE SIZE DETERMINAION USING DIODE LASER Aim To determine the size of the given particle using the laser source. Apparatus required Formula A laser source, laser grating, given particle, screen, scale, etc. Explanation of symbols Symbol Explanation Unit λ Wavelength of the laser source Å m Order of spectrum Unit Y m Distance of m th order from Zeroth order metre D 1 Distance between the particle and the screen metre Theory ` A device for producing spectra by diffraction is known as diffraction grating. While producing diffraction spectra using the particle, the size of the particle should be comparably equal to the wavelength of the source. The diffracted wave undergoes constructive and destructive interference effect. The intensities of the spectra depend up to the diffraction angle. By measuring the diffraction angle interms of orders of spectra. The wavelength of the given laser source and the size of the particle can be determined. 9

10 To fine the size of the given particle Wavelength of the given laser source = Å S.No. Order (m) LHS Y m RHS Mean Y m Y 2 m D 2 1 d Unit No. X10-2 m X10-2 m X10-2 m X10-4 m 2 X10-4 m 2 X10-2 m Metre

11 Procedure To find the size of the given particle Now the laser grating is removed and the size of the particle of be found is introduced. The laser source is switched ON and the light is made of fall on the particle. The screen is moved back and forth until the clear image of the spectrum is seen and the distance between the screen and the particle (D 1 ) is noted. Due to diffraction of laser light by the particle, different orders of spectrum are obtained as shown in fig.5. The positions Y 1, Y 2, Y 3 of the spots belonging to the first order, second order, third orders etc. on either side of the central maximum are noted in similar way as noted above. Then by using the given formula the size of the particle can be determined. Result: The size of the given particle =.. meter. VIVA VOCE 1. Define the term Diffraction, with its conditions. 2. What is meant by grating element? 3. Is the diffraction possible if laser light is replaced by ordinary light for the same particle? Explain. 4. What happens to the order of spectrum, if the distance between the particle and the screen is increased? 5. Will the laser undergo diffraction through ordinary grating? Explain. 6. What will happen to the order of spectrum if the size of the particle is decreased? 11

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14 Fig. 7 Diffraction Pattern Fig. 8 Angle of divergence. 14

15 Expt. No.: Date: 1. b. DETERMINATION OF WAVELENGTH OF LASER USING GRATING Aim To determine Wavelength of the given laser source, using a laser grating. Apparatus required Formula A laser source, laser grating, screen, scale, etc. Explanation of symbols Symbol Explanation Unit λ Wavelength of the laser source Å m Order of spectrum Unit X m Distance of m th order from Zeroth order metre D Distance between the particle and the screen metre N Number of rulings in the grating Lines/metre Theory A device for producing spectra by diffraction is known as diffraction grating. While producing diffraction spectra using the particle, the size of the particle should be comparably equal to the wavelength of the source. The diffracted wave undergoes constructive and destructive interference effect. The intensities of the spectra depend upto the diffraction angle. By measuring the diffraction angle interms of orders of spectra. The wavelength of the given laser source and the size of the particle can be determined. 15

16 (i) To find the wavelength of the laser source Number of rulings in the grating = S.No. Order (m) LHS X m RHS Mean X m X 2 m D 2 λ Unit No. X10-2 m X10-2 m X10-2 m X10-4 m 2 X10-4 m 2 X10-2 m Aº (ii) To find the Angle of Divergence (Ф) using Laser source S.No. Distance between laser and screen (X 10-2 m ) Radius of circular image (X 10-2 m ) Angle of divergence Ф = r 2 -r 1 /d 2 -d 1 (degree) 1 d 1 = r 1 = 2 d 2 = r 2 = 16

17 Procedure (i) To find wavelength of the laser source The laser source and the laser grating are mounted on separate stands as shown in fig.7. A fixed distance (D) is kept between the laser grating and the screen. The laser source is switched ON and the beam of laser is allowed to fall on the laser grating. The diffracted beams are collected on the screen. The diffracted beams are in the form of spots as shown in fig. 7. In the figure 7, the intensity of the irradiance is found to decrease, from zeroth order to higher orders, i.e. the first order is brighter than the second order and so on. The positions X 1, X 2, X 3 of the spots belonging to the first order, second order, third order etc., on either side of the central maximum are marked on the screen and is noted. The experiment is repeated for various values of D and the positions of the spots are noted. Then by using the given formula the wavelength of the source can be calculated and the mean is taken. (ii) To find the angle of a divergence (Ф) Angle of divergence given the angular spread of the laser beam. A simple diagrammatic explanation of finding the angle of divergence show in fig

18 CALCULATIONS: WORK SHEET 18

19 Result (a) (b) The wavelength of the given laser source = Å Angle of Divergence of the Laser beam=.. Degrees. VIVA VOCE 1. Define the term Diffraction, with its conditions. 2. What is meant by grating element? 3. Is the diffraction possible if laser light is replaced by ordinary light for the same particle? Explain. 4. What happens to the order of spectrum, if the distance between the particle and the screen is increased? 5. Will the laser undergo diffraction through ordinary grating? Explain. 6. What will happen to the order of spectrum if the size of the particle is decreased? 7. What is meant by Numerical aperture and Acceptance angle? 8. What is the principle used in the propagation of light through optical fibres? 19

20 What are the parts of an optical fibre? Fig 9. Numerical Aperture 20

21 Expt. No.: Date: 1. c. DETERMINATION OF ACCEPTANCE ANGLE OF OPTICAL FIBRE Aim To measure the numerical aperture and acceptance angle of the given optical fibre. Apparatus required Formula Optical fibre, numerical aperture measurement Jig., scale, etc. Numerical aperture of the given optical fibre NA = (No unit) Acceptance angle θ max = sin -1 (NA) degrees Explanation of symbols Symbol Explanation Unit d Distance between the tip of the optical fibre and the aperture of the Numerical Aperture (NA) Jig. metre r Radius of the circular opening in NA jig metre Theory Numerical Aperture (NA) and Acceptance Angle: It is the light collecting efficiency of the fibre and is the measure of the maximum amount of light that can be accepted by the fibre. Using Snell s law mathematically we can say NA = sin θ max = n n 2 Where, n 1 = refractive Index of core, n 2 = refractive index of cladding θ max = Acceptance angle of the fibre = sin- 1 (Numerical aperture) i.e. θ max = sin- 1 (NA) 21

22 Measurement of Numerical aperture S.No. Length of the given Distance between NA Jig opening and the Radius of the circular opening in Numerical Numerical aperture= fibre fibre (d) aperture Jig (r) Unit meter X10-3 m X10-2 m (No Unit) Acceptance angle (θ) 22

23 θ max = sin- 1 (NA) θ max =. degrees Procedure Measurement of Numerical aperture and Acceptance angle A known length of fibre is taken. One end of the fibre is connected to the laser source and the other end is connected to the numerical aperture (NA) Jig as shown in fig. 9. The source is switched ON. The opening in the NA jig is completely opened so that a circular red patch of laser light is observed on the screen. Now the opening in the NA Jig is slowly closed with the knob provided, so that at a particular points the circular light patch in the screen just cuts. The radius of the circular opening (r) of NA Jig at which the circular patch of light just cuts is measured. The distance between the NA jig opening and the fibre can be measured directly with the help of the calibration in NA jig. By substituting the values in the given formula the numerical aperture can be calculated. The same procedure can be adopted for various distances between the fibre and the opening of NA jig. The same procedure can be adopted for various length of fibre cable. By finding the mean of numerical aperture (NA) and substituting it in the given formula the acceptance angle can be determined. Result (i) The Numerical aperture of the given optical fibre =. (No unit) (ii) The acceptance angle of the given optical fibre = Degrees VIVA VOCE 1. What is meant by Numerical aperture and Acceptance angle? 2. What is the principle used in the propagation of light through optical fibres? 23

24 What are the parts of an optical fibre? 4. What is the type of the laser beam used in the experiment? WORK SHEET CALCULATIONS: 24

25 WORK SHEET CALCULATIONS: 25

26 Fig. 10. Air Wedge 26

27 Fig.11. Fringe pattern. Expt. No.: Date: 2. DETERMINATION OF THICKNESS OF A THIN WIRE - AIR WEDGE METHOD Aim To determine the thickness of a given thin wire (or) thin sheet of paper by forming interference fringes due to an air-wedge. Apparatus required Traveling microscope, two optically plane glass plates, 45 angle glass plate, given wire (or) thin paper, sodium vapour lamp, Transformer etc. Formula Thickness of the given wire (or) thin sheet of paper is given by t = Explanation of symbols Symbol Explanation Unit l Distance between edge of contact and the wire (or) paper metre λ Wavelength of the monochromatic source of light (5893 Å) metre β Mean fringe width metre Theory Two plane glass plates are inclined at an angle by introducing thin materials. (e.g.. hair), forming a 27

28 wedge shaped air film. This film is illuminated by sodium light, interference occurs between the two rays, one reflected from the front surface and the other obtained by internal reflection at the back surface. Since in the case of a wedge shaped film, thickness of the material remains constant only in direction parallel to the thin edge of the wedge, straight line fringes parallel to the edge of the wedge are obtained. (i) To find the band width (β) LC = cm TR = MSR + (VSC X LC) Order of the fringes Microscope reading Width of 15 Fringes MSR VSC TR fringes width (β) X10-2 m (Div) X10-2 m X10-2 m X10-2 m n n+5 n+10 n+15 n+20 n+25 n+30 n+35 n+40 n+45 n+50 Mean =. X 10-2 m 28

29 (ii) To find the distance between the edge of contact and the material of wire (or) paper. LC = cm TR = MSR + (VSC x LC) Position of the Microscope At the edge of contact Microscope reading MSR VSC TR x 10-2 m (Div) x 10-2 m (R1) l = R 1~R2 x 10-2 m At the edge of material of wire (or) paper (R2) Procedure Two optically plane glass plates are placed one over the other and tied by means of a rubber band at one end. The given material of wire (or) paper is introduced on the other end, so that an airwedge is formed between the plates as shown in fig.10. This set up is placed on the horizontal bed plate of the traveling microscope. Light from the sodium vapour lamp (S) is rendered parallel by means of a condensing lens (L). The parallel beam of light is incident on a plane glass plate (G) inclined at an angle of 45º and gets reflected. The reflected light is incident normally on the glass plates in contact Pc. Interference taken place between the light reflected from the top and bottom surfaces of the glass plates and is viewed through the traveling microscope (M). Hence large number of equally spaced dark and bright fringes are formed which are parallel to the edge of contact (fig. 11). The microscope is adjusted so that the bright (or) dark fringe near the edge of contact is made to coincide with the vertical cross wire and this is taken as the nth fringe. The reading from the horizontal scale of the traveling microscope is noted. The microscope is moved across the fringes using the horizontal traverse screw and the readings are taken when the vertical cross wire coincides with every successive 5 fringes (5, 10, 15.). The width of every 15 fringes is calculated and the width of one fringe is calculated. The mean of this gives the fringe width (β). The cross wire is fixed at the inner edge of the rubber band and the reading from the microscope is noted. Similarly reading from the microscope is noted keeping the cross wire at the edge of the material. The difference between these two values gives the value of l. Substituting β and l in the given formula, the thickness of the given material can be determined. 29

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31 Result The thickness of the given material =.. meter. VIVA VOCE 1. What is the principle behind the formation of fringes in Air wedge? 2. What is meant by an Air Wedge and explain how it can be formed? 3. What is meant by fringe width? 4. What is the theory of formation of thin films? Give examples. 31

32 What is the use of inserting 45 angled glass plate? 6. Why do we get straight line fringes in an airwedge? 7. Explain the reason for color formation in soap bubbles, when white light falls on it. 8. What happens to the fringe width, if the thickness of the material is increased? 9. What is the condition for the formation of bright fringes? 10. Why do we get bright and dark fringes alternatively? 32

33 Fig.12 Ultrasonic Interferometer Expt. No.: Date: 3. DETERMINATION OF VELOCITY OF SOUND AND COMPRESSIBILITY OF THE LIQUID - ULTRASONIC INTERFEROMETER Aim (i) To determine the velocity of Ultrasonic waves in the given liquid using Ultrasonic Interferometer. (ii) To determine the compressibility of the given liquid. Apparatus required Ultrasonic Interferometer, measuring cell, frequency generator, given liquid, etc. Formula (i) Velocity of Ultrasonic waves in the given liquid v = nλ ms -1 Where, Wavelength metre (or) Å (ii)compressibility of the given liquid m 2 / N 33

34 Explanation of symbols Symbol Explanation Unit n Frequency of the generator which excites the crystal Hertz λ Wavelength of the Ultrasonic metre ρ Density of the given liquid Kg/m 2 d Distance moved by the micrometer screw metre x Number of oscillations Unit Fig. 13 Distance moved by the reflector Vs Crystal current 34

35 Theory An Ultrasonic Interferometer is a simple and direct to determine the velocity of Ultrasonic waves in liquid with a high degree of accuracy. Here the high frequency generator generates variable frequency, which excited the Quartz Crystal placed at the bottom of the measuring cell (Fig. 12). The excited Quartz Crystal generates Ultrasonic waves in the experimental liquid. The liquid will now serve as an acoustical grating element. Hence when Ultrasonic waves passes through the rulings of grating, successive maxima and minima occurs, satisfying the condition for diffraction. Initial adjustments: In high frequency generator two knobs are provided for initial adjustments. One is marked with Adj (set) and the other with Gain (Sensitivity). With knob marked Adj the position of the needle on the ammeter is adjusted and with the knob marked Gain, the sensitivity of the instrument can be increased for greater deflection, if desired. Procedure The measuring cell is connected to the output terminal of the high frequency generator through a shielded cable. The cell is filled with the experimental liquid before switching ON the generator is switched ON, the Ultrasonic waves move normal form the Quartz Crystal till they are reflected back by the movable reflector plate. Hence, standing waves are formed in the liquid in-between the reflector plate and the quartz Crystal. The distance between the reflector and crystal is varied using the micrometer screw such that the anode current of the generator increases to a maximum and then decreases to a minimum and again increases to a maximum in the anode current is equal to half the wave length of the Ultrasonic waves in the liquid (Fig. 35

36 ). Therefore, by nothing the initial and final position of the micrometer screw for one complete oscillation (maxima minima- maxima) the distance moved by the reflector can be determined. To minimize the error, the distance (d) moved by the micrometer screw is noted for x number of oscillations (successive maxima), by noting the initial and final reading in the micrometer screw and is tabulated. From the total distance (d) moved by the micrometer screw and the number of oscillations(x), the wavelength of ultrasonic waves can be determined using the formula λ = 2d/x. From the value of λ and by noting the frequency of the generator (n), the velocity of the Ultrasonic waves can be calculated using the given formula. After determining the velocity of the Ultrasonic waves in liquids. The compressibility of the liquid is calculated using the given formula. 36

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38 Result (i)the velocity of Ultrasonic waves in the given liquid =. ms -1 (ii)compressibility of the given liquid =. m 2 N -1 VIVA VOCE 1. What is meant by Compressibility? 2. Explain the terms stress and strain. 3. What is the frequency range of Ultrasonics? 4. What is mean by acoustical grating? 5. Explain the principle of determining the compressibility of liquids. 6. What is meant by nodes and Antinodes? 7. What do you understand by the term Over tones? 8. Is Ultrasonic wave, an Electromagnetic wave? Explain. 9. What are the various liquids that can be used for finding the compressibility using Ultrasonic interferometer? 10. What type crystal is thrown into vibrations in the case of Ultrasonic interferometer? 38

39 WORK SHEET CALCULATIONS: 39

40 WORK SHEET CALCULATIONS: 40

41 LC = 1 λ= 5893 A Diffracted ray readings Left (R1) Right (R2) (i) To find the number of lines per metre on the grating (N) Order of the spectrum (n) = Total Reading = MSR + (VSCXLC) MSR Vernier A (VA) VSC TR MSR Vernier B (VB) VSC TR 2 θ= R1-R2 VA VB Mean θ = 2θ/2 VA VB Mean θ N = sin θ/nλ degrees divisions degrees degrees divisions degrees degrees degrees degrees degrees degrees Lines / m 41

42 Expt. No.: Date: 4. DETERMINATION OF WAVELENGTH OF MERCURY SPECTRUM - SPECTROMETER GRATING Aim To determine the wavelength of the mercury (Hg) spectrum by standardizing the plane transmission grating. Apparatus required Spectrometer, plane transmission grating, mercury vapour lamp, sodium vapour lamp, spirit level, lens, torch light etc. Formula (i) The number of lines drawn on the grating per meter is given by lines /meter (ii)the wavelength of the prominent lines of the mercury spectrum is given by Explanation of symbols Symbol Explanation Unit Å n Order of spectrum Unit λ Wavelength of the Sodium vapour lamp (5893 Å) Metre (or) Å θ Angle of diffraction Degree 42

43 Fig. 14. Position of the Grating Reflected Ray Fig.15. Spectrometer Grating First to Get order Diffraction 43

44 Procedure (i) Adjustment of grating for normal incidence Preliminary adjustments of the spectrometer are made. The grating (G) is mounted on the grating table with its ruled surface facing the collimator. The slit is illuminated by a source of light (either sodium (or) mercury vapour lamp) and is made to coincide with the vertical cross wire. (The vernier scales are adjusted to read 0 and 180 for the direct ray. The telescope is rotated through an angle 90 and is fixed. The grating table is adjusted until the image coincides with the vertical cross wire. Both the grating table and the telescope are fixed at this position (fig.14). Now rotate the vernier tables through 45 in the same direction in which the telescope has been previously rotated. The light from the collimator incidents normally (perpendicularly) on the grating. The telescope is released and is brought on line with the direct image of the slit. Now the grating is said to be in the normal incidence position (fig. 15). (ii) Standardization of grating (To find the number of lines drawn in the grating per meter) The slit is illuminated by sodium vapour lamp. The telescope is released to get the diffracted image of the first order on the left side of the central direct image. The readings are tabulated from the two verniers V A and V B. Similarly readings are taken for the right side of the central direct image (fig. 15). The difference between the two readings gives 2θ, where θ is the angle of first order diffraction. The number of lines per meter (N) of the grating is calculated using the given formula. The experiment is repeated for the second order and the readings are tabulated. (iii) Determination of wavelength of the mercury spectrum The sodium vapour lamp is replaced by mercury vapour lamp. The diffracted images of the first order are seen on either side of the central direct image (fig.15). As before the readings are tabulated by coinciding the vertical cross wire with the prominent lines namely violet, blue, blueish green, green, yellow, red of the mercury spectrum. The difference between the readings give 2θ, from this θ can be found. The wavelength of each spectral line is calculated using the given formula. 44

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46 Result (i) (ii) Number of lines drawn in the grating per meter =.. Lines/ meter. Wavelength of various spectral lines of the mercury spectrum are λ V =.. Aº λ B =.. Aº λ BG =.. Aº λ G =.. Aº λ Y =.. Aº λ R =.. Aº VIVA - VOCE 1. How many rulings are there in the grating element given? 2. What is the condition for diffraction? 3. What is the difference between reflection and scattering? 4. What do you understand by the term least count? 5. What is the difference between transmission and reflection grating? 6. Why the skies appear red during sunset? 7. What is meant by dispersion? 8. Define wave packet. 9. What is the use of collimator and telescope? 10. How the astronomical telescopes differ from ordinary telescope? 46

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49 Fig. 16 Lee s Disc apparatus arrangement (i) To find (dθ/dt)θ 2 θ 1 =.. C θ 2 =.. C S.No Temperature Time Taken C Kelvin Sec. 1 θ θ θ θ θ θ 2 7 θ θ θ θ θ

50 Expt. No.: Date: 5. DETERMINATION OF THERMAL CONDUCTIVITY OF A BAD CONDUCTOR - LEE S DISC METHOD. Aim To determine the thermal conductivity of a bad conductor using Lee s disc apparatus. Apparatus required Lee s disc apparatus, two thermometers, bad conductor, stop watch, steam boiler, vernier caliper, screw gauge, biscuit balance etc. Formula Thermal conductivity of the given band conductor Explanation of symbols Symbol Explanation Unit M Mass of the metallic disc Kg S Specific heat capacity of the material of the disc J/Kg/K (dθ/dt)θ 2 Rate of cooling at steady temperature θ 2 Kelvin θ 1 Steady temperature of the steam chamber Kelvin θ 2 Steady temperature of the metallic disc Kelvin R Radius of the metallic disc metre h Thickness of the metallic disc metre x Thickness of the bad conductor metre 50

51 (ii) To find the diameter of the metallic disc Fig. 17 Model Graph. LC = 0.01 cm ZE =. ZC =. x 10-2 m S.No. Main Scale Reading (MSR) Vernier Scale Coincidence (VSC) Observed Reading OR=MSR+(VSCXLC) Correct Reading CR = OR±ZC Unit X 10-2 m Div. X 10-2 m X 10-2 m Mean =.. x 10-2 m 51

52 Description Lee s disc apparatus consists of a brass metal disc (B) suspended horizontally by three strings form a stand. A hollow steam chamber (A) with inlet and outlet for steam is placed above. The given bad conductor is placed between them. Two thermometers T 1 & T 2 are inserted to measure the temperatures of A and B respectively. Procedure The experimental arrangement is as shown in fig 16. Steam is allowed to pass through the steam chamber. The temperature indicated by two thermometers start rising. After 30 minutes a steady state is reached (i.e) the temperature of the lower disc will no longer rises. At this stage, steady temperatures θ 1 and θ 2 are recorded from the thermometers T 1 and T 2. Now the cardboard is removed and the lower disc is heated directly by keeping it in contact with the steam chamber. When the temperature of the lower disc attains a value of about 10 C more than its steady state temperature, the chamber is removed and the lower disc is allowed to cool down on its own accord. When the temperature of the disc reaches 5 C above the steady temperature (θ 2 ) of the disc i.e., (θ 2 +5 C), a stop watch is started and the time is noted for every 1 C fall of temperature until the metallic disc attains temperature (θ 2-5 C). The thickness and radius of the metallic disc is found using screw gauge and vernier caliper respectively. The thickness of the bad conductor is found using screw gauge. The mass of the metallic disc is found by using biscuit balance. The readings are tabulated in the tabular column. Graph A graph is drawn by taking time along the x-axis and the temperature along y-axis (fig. 17) Cooling curve is drawn. From the cooling curve dθ/dt is calculated by drawing a triangle by taking 0.5 C above and 0.5 C below the steady temperature θ 2. Substituting this dθ/dt in the given formula, thermal conductivity of the card board can be calculated. 52

53 (iii) To find the thickness of the metallic disc LC = 0.01 mm ZE =. ZC =. x 10-3 m S.No. Pitch Scale Reading (PSR) Head Scale Coincidence (HSC) Observed Reading OR=PSR+(HSCXLC) Correct Reading CR = OR±ZC Unit X 10-3 m Div. X 10-3 m X 10-3 m Mean =.. x 10-3 m (i) To find the thickness of the Bad Conductor LC = 0.01 mm ZE =. ZC =. x 10-3 m S.No. Pitch Scale Reading (PSR) Head Scale Coincidence (HSC) Observed Reading OR=PSR+(HSCXLC) Correct Reading CR = OR±ZC Unit X 10-3 m Div. X 10-3 m X 10-3 m Mean =.. x 10-3 m 53

54 Result Thermal Conductivity of given Bad Conductor =. W/m/K VIVA - VOCE 1. What do you understand by the term conduction, convection and radiation? 2. What is meant by thermal conductivity? 3. Name any four bad conductors? 4. What do you understand by the term steady state? 5. What is meant by Rate of Cooling? 6. What is the use of cooling the slab and noting the time? 7. What happen to the thermal conductivity if the thickness of the given bad conductor is increased? 8. Is the diameter of the bad conductor should match diameter of the disc (D) and the steam chamber (S)? Why? 9. Will there be any change in thermal conductivity if the area of cross section of bad conductor is decreased: Justify. 10. State some of the applications of bad conductors. 54

55 WORK SHEET CALCULATIONS: 55

56 WORK SHEET CALCULATIONS: 56

57 Fig 18 a. Top view of the B-H Curve Unit Fig 18b. Hysteresis loop 57

58 Expt. No.: Date: 6. DETERMINATION OF HYSTERESIS LOSS IN A FERROMAGNETIC MATERIAL. Aim To determine the hysteresis loss in the transformer core using B-H curve unit. Apparatus required CRO, B-H curve unit, patch cords Formula Energy loss = Explanation of symbols Symbol Explanation Unit Number of turns in the primary coil - Number of turns in the secondary coil - A Area of cross section of core m 2 L Length of the core m S V Steady temperature of the metallic disc - S H Horizontal sensitivity of the CRO - DESCRIPTION The experimental arrangement is shown in the figure 18a. One of the specimens used in the unit is made using transformer stampings. There are two windings on the specimen (primary and secondary). The primary is fed to low A.C voltage (50Hz). This produces a magnetic field H in the specimen. The voltage across R 1 (resistance connected in series with primary) is proportional to the magnetic field. It is given to the imput of the CRO. The A.C magnetic field induces a voltage in the secondary coil. The voltage induced is proportional to db/dt. This voltage is applied to passive integrating circuit. The output of the integrator is proportional to B and fed to the vertical input of the 58

59 CRO. As a result of the application of voltage proportional to H the horizontal axis and a voltage proportional to B is the vertical axis, the loop is formed as shown in fig 18b. S.No. N 1 N 2 R 1 ohm R 2 ohm S V S H Area of the loop Energy loss Observations Number of turns in the primary N 1 = Number of terms in the secondary N 2 = R 1 = ohm R 2 = ohm C 2 = µf S V = Vm -1 S H = Vm -1 Calculation Area o f the loop = m 2 59

60 Energy loss = PROCEDURE The unit one to force the B-H loop (hysteresis) of a ferromagnetic specimen using a CRO is shown in figure. A measurement of the area of the loop leads to the evaluation of the energy loss in the specimen. The top view of the unit is shown in the figure. There are 12 terminals on the panel; sin patch cords are supplied with the kit. The value of R1 can be selected connecting terminal D to B or C (A-D = 50 ohm; B-D = 150 ohm; C-D = 50 ohm) A is connected to D. The primary terminals of the specimen is connected to p, p secondary to s, s terminals. The CRO is calibrated as per the instructions given the Instruction Manual of CRO. CRO is adjusted to work on external mode (the time base is switched off). The horizontal and vertical position controls are adjusted such that the spot is at the centre of the CRO screen. The terminal marked GND is connected to the ground of the CRO. The H is connected to the Horizontal input to the ground of the CRO. The H is connected to the Horizontal input of the CRO. The terminals V are switched on. The hysteresis loop is formal. The horizontal and vertical gains are adjusted such that the loop occupies maximum area of the screen of the CRO. Once this adjustment is made, the gain controls should not be disturbed. The loop is traced on a translucent graph paper. The area of the loop is estimated. The connections from CRO are removed without disturbing the horizontal and vertical gain controls. The vertical sensitivity of the CRO is determined by applying a known A.C voltage say 1 volt (peak to peak). If the spot deflects by X cms for 1 volt, the vertical sensitivity is 1/X x 10-2 (volt/m). Let it be dv. The horizontal sensibility of CRO is determined by applying a known A.C. voltage say 1 volt (peak to peak). Let the horizontal sensitivity be S H (volt/m). The transformer core may be replaced by ferrite ring and hysteresis loss in ferrite core can be found. 60

61 WORK SHEET CALCULATIONS: 61

62 Result: Energy loss =. Joules cycle -1 m

63 Fig.19 Non Uniform Bending Model Graph To find M/y LC = cm TR = MSR +(VSCXLC) S.No Distance between Knife edges (l) Load (M) Microscope Reading Increasing Load Decreasing Load MSR VSC TR MSR VSC TR Mean Depress ion (y) M/y Unit X 10-2 m X 10-3 Kg X 10-2 m Div X 10-2 m X 10-2 m Div X 10-2 m X 10-2 m X 10-2 m X 10-1 Kg m -1 1 W 2 W+50 3 W W W W+250 Mean M/y =..Kg/m 63

64 Expt. No.: Date: 7. DETERNINATION OF YOUNG S MODULUS OF THE MATERIAL NON UNIFORM BENDING Aim To determine the young s modulus of the given material of the beam by Non Uniform bending. Apparatus requited A long uniform beam usually a meter scale, travelling microscope, pin, weight hanger with slotted weights, vernier calipers, Screw gauge, knife edges etc., Formula The Young s Modulus of the given material of the beam By Calculation method Nm -2 By Graphical method Nm -2 Explanation of symbols Symbol Explanation Unit g Acceleration due to gravity m/s 2 l Distance between Knife edge meter b Breadth of the beam meter d Thickness of the beam meter y Depression produced for M kg of load meter M Load applied Kg k Slope 1/k from graph Kg m -1 64

65 By Graphical method to find h/m AXIS W-(W+50) W-(W+100) W-(W+150) W-(W+200) W-(W+250) X (M) Y ( h) To find Breadth (b) of the beam using vernier calipers LC = 0.01cm ZE =. ZC =. x 10-2 m S.No. Main Scale Reading (MSR) Vernier Scale Coincidence (VSC) Observed Reading OR=MSR+(VSCXLC) Correct Reading CR = OR±ZC Unit X 10-2 m Div. X 10-2 m X 10-2 m Mean b =.. x 10-2 m To find the thickness (d) of the beam using screw gauge. ZE =. LC = 0.01 mm ZC =. x 10-3 m S.No. Pitch Scale Reading (PSR) Head Scale Coincidence (HSC) Observed Reading OR=PSR+(HSCXLC) Correct Reading CR = OR±ZC Unit X 10-3 m Div. X 10-3 m X 10-3 m

66 Mean d =.. x 10-3 m Procedure The given beam is placed on the two knife edges (A and B) at a distance say 70 cm or 80 cm. A weight hanger is suspended at the centre(c) of the beam and a pin is fixed vertically on the frame of the hanger as shown in fig.19. Taking the weight hanger alone as the dead load the tip o the pin is focused by the microscope, and is adjusted in such a way that the tip of the pin just touches the horizontal cross wire. The reading on the vertical scale is noted. Now the weight is added in steps of 50 grams. Each time the tip of the pin is made to touch the horizontal cross wire and the readings are noted from the vertical scale of the microscope. The procedure is followed until the maximum load is reached. The same procedure is repeated by unloading the weight in steps of same 50 grams and the readings are tabulated in the tabular column. From the readings the mean of (M/y) is calculated. The thickness and the breadth of the beam are measured using screw gauge and vernier calipers respectively and are tabulated. By substituting the values in the given formula. The young s modulus of the material of the beam can be calculated. Graph A Graph is drawn taking load (M) along x axis and depression y along y axis as shown in figure. The slope of the graph gives the value K = y/m. Substituting the value of the slope in the given formula, the Young s modulus can be calculated. Result The Young s modulus of the given material of the beam by calculation Y =. Nm -2 by Graph Y =. Nm -2 VIVA - VOCE 1. What is meant by non uniform bending? 2. Define neutral axis. 3. Name any two methods used to determine the young s modulus of the beam. 4. Define elasticity. 5. Will there be any change in young s modulus of the material, if its thickness is increased? Justify. 6. What are the basic assumptions made from the theory of bending? 7. Why iron girders used in buildings are made in the form of I section? 66

67 8. What is the use of keeping an optimum of 0.7 to 0.8 meter distance between the knife edges? 9. Define elastic limit. 10. What is meant by elastic constants? WORK SHEET CALCULATIONS: 67

68 WORK SHEET CALCULATIONS: 68

69 MODEL GRAPH Fig.20 Band gap 69

70 Fig.21 Model graph Expt. No.: Date: 8. DETERMINATION OF BAND GAP OF A SEMICONDUCTOR MATERIAL Aim To determine the band gap energy of a semiconductor by studying the variation of reverse saturation current of a point contact diode at any temperature. Apparatus required Point contact diode, heating arrangement to heat the diode, ammeter, thermometer etc. Formula Band Gap Energy E g = x Slope ev voltmeter, Where Explanation of symbols 70

71 Symbol Explanation Unit I s Saturation Current µa T Absolute Temperature Kelvin Theory For a semiconductor diode at 0 K the valence band is completely filled and the conduction band is completely filled and the conduction band is empty and it behaves as an insulator. If the temperature is increased, some of the valence electrons gains thermal energy greater than the forbidden band gap energy (Eg) and it moves to conduction band, which constitutes some current to flow through the semiconductor diode. (i) Measurement of current for various temperatures Power supply =.. Volts S.No. Temperature in Temperature in centigrade Kelvin 1000/T I s Log I s Unit C K K -1 X 10-6 Amp Amp

72 Band Gap energy Eg = x ( ) ev Eg = x Slope ev Eg = ev Procedure The circuit is given as shown in fig.20. The point contact diode and the thermometer are immersed in a water (or) oil bath, in such a way that the thermometer is kept nearby the diode. The power supply is kept constant (say 3 volts). The heating mantle is switched ON and the oil bath is heated up to 70 C. Now the heating mantle is switched OFF and the oil bath is allowed to cool slowly. For every one degree fall of temperature the microammeter reading (I s ) is noted. A graph is plotted taking 1000/T along X axis and log I s along negative Y axis, (Since I s is in the order of micro-amperes, log Is value will come in negative). A straight line is obtained as shown in model graph (fig.21). By finding the slope of the straight line, the band gap energy can be calculated using the given formula. The same procedure can be repeated for various constant power supplies (4volts, 5 volts) Result The band gap energy of the given diode is =.. ev 72

73 VIVA - VOCE 1. What is meant by conduction band and valence band? 2. Explain the term Band gap? 3. What are the types of semiconductors? 4. What do you understand by the term Fermi Level? 5. What is the band gap energy for germanium and silicon? 6. What is the effect of temperature over a semiconductor? 7. What is the principle used in finding the band gap energy of a semiconductor? 8. What is the use of keeping the diode inside the oil bath? 9. Shall the oil bath be replaced by water bath? State the reason. 10. What is the biasing of the semiconductor diode in the band gap experiment? WORK SHEET CALCULATIONS: 73

74 CALCULATIONS: WORK SHEET 74

75 Circuit diagram Fig 22.(a) Carey Foster s Bridge 75

76 Fig. 22(b) Bridge Equivalent Expt. No.: Date: 9. DETERMINATION OF SPECIFIC RESISTANCE OF GIVEN COIL OF WIRE CAREY FOSTERS BRIDGE Aim To determination of the specific resistance or resistivity of the material of the coil. Apparatus requited Bridge wire resistance coil, Battery, 4 & 2 dial resistance boxes, copper strips, galvanometer, High resistance, key, Jockey, etc., Formula Resistance per unit length of the bridge wire Specific resistance or resistivity = SA/l ohm meter 76

77 Explanation of symbols Symbol Explanation Unit Resistance per unit length of the bridge wire Ohm / Meter R Resistance introduced in the variable box R Ohm l 1, l 2 The balancing lengths Meter S Resistance of the coil (to be determined) Ohm l Length of the coil Meter A Area of the cross section of the coil Meter 2 Table No: 1 To determine the resistance per unit length of the bridge wire. S.No. Fractional Balancing Length Resistance R ohm l 1 m l 2 m = R/ (l 2 -l 1 ) ohm/ meter

78 Mean =.. Procedure Carey Foster s bridge is more useful for comparing two nearly equal resistances or to determine unknown resistance. It is the modified form of the meter bridge and works on the principle of Wheatstone s bridge. Since the end resistances are eliminated, the unknown resistances can be determined very accurately. It consists of a uniform resistance wire AB, of one meter long. Normally the wire is made from managing which has zero temperature coefficient of resistance. The ends of the wire are soldered to two thick L-Shaped cooper strips of negligible resistance. There are three more copper strips which are fixed on the wooden board between the first two L-shaped strips so as to form four gaps 1, 2, 3 and as shown in fig22(a). The copper strips are provided with binding screws for electrical connection. Two known equal standard resistances P & Q are connected in gaps 2 and 3 respectively and a variable resistance box R and the given unknown resistance S are connected in gaps 1 and 4 respectively. Battery with a key and a galvanometer with a safety high resistance and jockey are connected as shown in fig 22a. Contact can be made at any point on the bridge wire by 78

79 means of jockey. A meter scale is fixed on the board parallel to the length of the wire so as to take readings directly. Experiment to determine the resistance of the given coil of wire: Having introduced a value R in the resistance box, the circuit is closed and the balancing point J on the bridge wire where there is no deflection in the galvanometer is determined. The balancing length l 1 is measured from the point A. The experiment is repeated by interchanging R and S and the balancing length l 2 is noted. The experiment is repeated by varying the known resistance R and in each case l 1 and l 2 are measured. Determination of : To determine the resistance per unit length of the bridge wire, the resistance S is replaced by a thick copper strip (i.e. S = 0) and the balancing length l 1 is determined using fractional resistance in R. Now by interchanging R and copper strip (S = 0, the balancing length l 2 is determined. 0 = R+ (l 1 -l 2 ) = R/ (l 2 -l 1 ) ohm / meter. Table: 2 To find the specific resistance or resistivity of the material of the coil Balancing Length S= = R+ (l 1 -l 2 ) S.No. Resistance R ohm l 1 m l 2 m Ohm

80 Mean S =. Ohm Now the unknown resistance is inserted in the bridge circuit instead of copper stip. The bridge will have the maximum sensitivity when S = R and hence the error in measuring the value of S is also minimum in that condition. So, after inserting the unknown resistance in the bridge arm, the jockey is pressed at the 50 th cm of the bridge wire and the value of R is varied. The value of R at which there is null deflecting in the galvanometer is noted. This will give the approximate resistance of the unknown resistance. Let it be X ohm. Now, the value of R is varied is steps of 0.2 ohm between (X+1) ohm to (X-1) ohm and correspondingly the balancing lengths l 1 and l 2 are determined and tabulated in the table no 2. Mean of the last column in the tabular column number 1 indicated the resistance of the bridge wire per unit length (p) and that value is substituted in equation in the tabular column number 2. The mean of the last column in the tabular column number 2 gives the value of the unknown resistance of the given coil of wire. Special cases: 80

81 (i)determination of the specific resistance or resistivity of the material of the coil: Specific resistance or resistivity = SA/l ohm meter where S is the resistance of coil, A and l are the area of cross section and the length of the wire in the coil respectively. Using a screw gauge, the radius of the wire can be determined. Hence the area of cross section a = πr 2 can be determined. Using the above formula the resistivity of the material of the coil wire can be determined. Result 1. Resistance per unit length of the bridge wire =. Ohm / Meter 2. Specific resistance of resistivity of the material of the coil =.. Ohm - Meter VIVA - VOCE 1. State the Principle of wheatstone s Bridge 2. What do you mean by the term balancing length? CALCULATIONS: WORK SHEET 81

82 WORK SHEET CALCULATIONS: 82

83 Fig. 23. Coefficient of viscosity - poiseuilles flow method 83

84 (i) Measurement of time for liquid flow h 0 =.. x 10-2 metre S.No. Burette reading Time note while crossing level Range Time for flow of 5 cc liquid Height of initial reading h 1 Height of final reading h 2 Pressure head h=(h 1 +h 2 /2)- h 0 ht Unit cc Seconds X10-2 m seconds X10-2 m X10-2 m X10-2 m X10-2 m Expt. No.: Mean ht = X10-2 m -sec Date: 10. DETERMINATION OF VISCOSITY OF LIQUID - POISEUILLES METHOD Aim To determine the coefficient of viscosity of the given liquid by poiseuilles flow method. Apparatus required Formula A graduated burette, rubber tube, capillary tube, pinch cork, etc., Coefficient of viscosity (Nsm -2 ) 84

85 Explanation of symbols Symbol Explanation Unit g Acceleration due to gravity m/s 2 ρ Density of the liquid Kg/m 3 r Radius of the capillary tube metre v Volume of the liquid collected metre 3 h metre h 1 Height from table to initial level of water in the burette metre h 2 Height from table to final level of water in the burette metre h o Height from table to mid portion of capillary tube metre t Time taken for the liquid flow Second l Length of the capillary tube metre Fig 24. Radius of Capillary Tube To find the radius of the bore of the capillary tube LC = cm TR = MSR+ (VSCXLC) 85

86 Position Microscope Reading Radius (r) MSR VSC TR X10-2 m Div X10-2 m X10-2 m Left V1 r = V 1 ~V 2 Right V2 Top H1 r = H 1 ~H 2 Bottom H2 Procedure The burette is held vertically on a retort stand. A capillary tube is attached to the lower end of the burette using a rubber tube as shown in fig 23. The burette is filled with the given liquid. The capillary tube is made horizontal and the liquid is allowed to flow freely through it. When the liquid comes to a known height (h 1 ), which is the height measured from the axis of the capillary tube, the stop watch is started. The stop watch is stopped when the liquid comes to another level which is of height h 2 from the axis of the capillary tube. Then the driving height is given by. The driving height, volume of the liquid and the time taken for flow of liquid are noted in the tabular column. The experiment is repeated for various known heights of the liquid and the time taken is noted. The mean of (ht/v) is taken. The radius of the bore of the capillary tube figure. Can be found by using a travelling microscope by mounting the capillary tube over a stand. Substituting the above data in the given formula, the coefficient of viscosity can be calculated. 86

87 Result: The coefficient of viscosity of the given liquid =.. Nsm -2. VIVA VOCE 1. Define coefficient of viscosity 2. What is meant by capillary rise, give some practical applications? 3. What will happen to the viscosity if the density of the liquid is increased? 4. Name any two highly viscous liquid. 5. Name any two methods used to determine the viscosity. 6. What will happen to the viscosity of the liquid if the temperature of the liquid is increased? Justify your answer. 7. Define stream line motion and turbulent motion. 8. State the relation between pressure and viscosity. 9. Define critical velocity. 10. What is meant by velocity gradient? WORK SHEET CALCULATIONS: 87

88 CALCULATIONS: WORK SHEET 88

89 89

90 Fig 25. Angle of Prism (A) (i) To find the angle of Prism (A) LC = 1 Total Reading (TR) = MSR + (VSCXLC) VERNIER - A VERNIER B 2A = R 1 ~ R 2 A Reflected MSR VSC TR MSR VSC TR V A V B V A V B Image (deg) (div) (deg) (deg) (div) (deg) (deg) (deg) (deg) (deg) Face I (Left) (R 1 ) (R 1 ) Face 2 (Right) (R 2 ) (R 2 ) Expt. No.: Mean A = Date: 90

91 11. SPECTROMETER - DISPERSIVE POWER OF A PRISM Aim To determine the refractive index and hence the dispersive power of the given prism using spectrometer. Apparatus required Spectrometer, glass prism, sodium vapour lamp, transformer, mercury vapour lamp, pencil torch, lens, spirit level etc., Formula Refractive index of the given prism is given by (No unit) Dispersive power of the prism in the wavelength region of λ 1 and λ 2 is = (No unit) Explanation of symbols Symbol Explanation Unit A Angle of the prism degrees D Angle of minimum deviation degrees µ 1 Refractive index of the prism for 1 st colour No unit µ 2 Refractive index of the prism for 2 nd colour No unit 91

92 Fig 26. Angle of Minimum Deviation (D) 92

93 Procedure To find the angle of Prism (A) To initial adjustments of the spectrometer is made. The silt is illuminated by yellow light from the sodium vapour lamp. The given prism is mounted on the prism table such that light emerging from the collimator should be made to incident on both the refracting faces of the prism as shown in fig 25. The telescope is rotated (left or right) to catch the image of the slit reflected by one of the refracting face of the prism. The telescope is fixed. By adjusting the tangential screw, the image is made to coincide with the vertical cross wire. The main scale and the vernier scale readings are noted from both the vernier A (V A ) and vernier B (V B ). Similarly readings are taken for the image reflected by other refracting face of the prism. The difference between the two readings gives 2A, where A is the angle of prism. To find the angle of minimum deviation (D) and dispersive power The prism is mounted such that light emerging from the collimator is incident on one of the refracting face of the prism. The telescope is slowly rotated to catch the refracted image of any one of the colour (say colour -1 (violet)) which emerges from other refracting face of the prism. Now by viewing through the telescope the prism table is slightly rotated in such a way that the violet image moves towards the direct ray and at a particular position it retraces its original path. This position is called MINIMUM DEVIATION POSITION (fig 26). The prism table is fixed and hence now all the colours in the adjusted to coincide with the image of each and every colour with the vertical cross wire and the readings are noted. The prism is removed and the direct ray reading is noted. The difference between the direct ray and the refracted ray readings for each and every colour gives the angle of minimum deviation (D) for that respective colour. Then, by substituting the values of D and A in the given formula, the refractive indices (µ) for each and every colour can be calculated. Finally by choosing any one of the colour refractive index as µ 1 and the any other as µ 2 the dispersive power of the prism is calculated using the given formula. Similarly for various values of µ 1 and µ 2 the dispersive powers are calculated and the mean of all the dispersive powers is calculated. 93

94 (ii)to find the angle of minimum deviation (D) and refractive index (µ) LC = 1 TR = MSR+ (VSCXLC) Angle of Prism (A) =.. Position Direct VERNIER - A VERNIER B D = R 1 ~ R 2 Mean (D) MSR VSC TR MSR VSC TR V A V B (deg) (div) (deg) (deg) (div) (deg) (deg) (deg) (deg) µ = sin[(a+d)/ 2]/sin [A/2] Ray (R1) (R1) Violet I Violet - (R2) (R2) II (R2) (R2) Blue Blueish (R2) (R2) Green (R2) (R2) Green Yellow (R2) (R2) I (R2) (R2) Yellow - II (R2) (R2) Red (R2) (R2) 94

95 Result: (i) Angle of the given prism (A) =. degrees (ii) Angle of the minimum deviation (D) =.. degrees (iii) The refractive index of the material of the given prism (µ) =...(No unit) (iv) Mean dispersive power of the prism =.. (No unit) VIVA VOCE 1. What is meant by a spectrum? 2. Define dispersive power. 3. What are the initial adjustments to be made before using the spectrometer? 4. Define angle of prism. 5. What is meant by minimum deviation? 6. Define reflection, refraction and transmission of light. 7. Define refractive index of the prism. 8. Is sodium lamp a monochromatic source? Why? 9. What are the applications of a spectrometer? 10. What is meant by Least Count give its significance? 95

96 CALCULATIONS: WORK SHEET 96

97 WORK SHEET CALCULATIONS: 97

98 Fig 27. Uniform Bending (i) To find M/h LC = cm TR = MSR + (VSCXLC) S.N o Distance Load Microscope Reading between (M) Increasing Load Decreasing Load Knife edges (l) MSR VSC TR MSR VSC TR Mea n Elevat ion (h) M/h Unit X 10-2 m X 10-3 Kg 1 W X 10-2 m Div X 10-2 m X 10-2 m Div X 10-2 m X 10-2 m X 10-2 m X 10-1 Kg m -1 2 W+50 3 W W W W+250 Mean = 98

99 Expt. No.: Date: 12. DETERNINATION OF YOUNG S MODULUS OF THE MATERIAL UNIFORM BENDING Aim To determine the young s modulus of the given material of the beam by uniform bending. Apparatus required A long uniform beam usually a meter scale, travelling microscope, pin, weight hanger with slotted weights (2 sets), vernier calipers, Screw gauge, knife edges etc., Formula The Young s Modulus of the given material of the beam By Calculation method Nm -2 By Graphical method Nm -2 Explanation of symbols Symbol Explanation Unit g Acceleration due to gravity m/s 2 l Distance between Knife edge metre b Breadth of the beam metre d Thickness of the beam metre h Elevation of the midpoint of the beam above the knife-edge metre M Load applied Kg k Slope h/m from graph m Kg -1 a Distance between knife edge and slotted weight hanger in the beam metre 99

100 By Graphical method to find h/m AXIS W-(W+50) W-(W+100) W-(W+150) W-(W+200) W-(W+250) X (M) Y ( h) (i) To find Breadth (b) of the beam using vernier calipers ZE =. LC = 0.01 cm ZC =. x 10-2 m S.No. Main Scale Reading (MSR) Vernier Scale Coincidence (VSC) Observed Reading OR=MSR+(VSCXLC) Correct Reading CR = OR±ZC Unit X 10-2 m Div. X 10-2 m X 10-2 m Mean b =.. x 10-2 m To find the thickness (d) of the beam using screw gauge. LC = 0.01 mm ZE =. ZC =. x 10-3 m S.No. Pitch Scale Reading (PSR) Head Scale Coincidence (HSC) Observed Reading OR=PSR+(HSCXLC) Correct Reading CR = OR±ZC Unit X 10-3 m Div. X 10-3 m X 10-3 m Mean d =.. x 10-3 m 100

101 Procedure The given beam is supported on the two knife edges (A and B) in the same horizontal level, equal lengths projecting beyond each knife- edge. The weight hanger are attached at two points equally distant (a) beyond the knife-edges. A pin is fixed exactly at the mid-point of the beam. A travelling microscope capable of vertical motion is arranged in front of the pin and focused on its tip. The tip is made to coincide with the horizontal cross-wire. Loads are added to both the hangers in steps of M (50 gms) and the microscope is moved up so that the tip of the image of the pin just coincides with the horizontal cross-wire in each case and the MSR, VSC readings are noted. The same procedure is repeated by unloading the weight in steps of same 50 grams and the readings are tabulated in the tabular column. From the readings the mean of (M/h) is calculated. The thickness and the breadth of the beam are measured using screw gauge and vernier calipers respectively and are tabulated. By substituting the values in the given formula the Young s modulus of the material of the beam can be calculated. Graph A graph is drawn taking load (M) along x axis and elevation h along y axis as shown in figure. The slope of the graph gives the value K=h/M. Substituting the values of the slope in the given formula, the Young s modulus can be calculated. Result The Young s modulus of the given material of the beam By calculation Y =. Nm -2 By Graph Y =. Nm -2 VIVA - VOCE 1. What is meant by uniform bending? 2. Define neutral axis. 3. Name any two methods used to determine the young s modulus of the beam. 4. Define elasticity. 5. Will there be any change in young s modulus of the material, if its thickness is increased? Justify. 6. What are the basic assumptions made from the theory of bending? 7. Why iron girders used in buildings are made in the form of I section? 8. What is the use of keeping an optimum of 0.7 to 0.8 meter distance between the knife edges? 9. Define elastic limit. 10. What is meant by elastic constants? 101

102 CALCULATIONS: WORK SHEET 102

103 WORK SHEET CALCULATIONS: 103

104 (i)to find L/T 2 Fig 28. Torsional Pendulum S.No Length of the Time for 10 oscillations suspend wire (L) Trail - 1 Trail - 2 Mean Time period T T 2 L/T 2 Unit X 10-2 m sec sec sec Sec s 2 Ms Mean L/T 2 =.. ms