CMR INSTITUTE OF TECHNOLOGY
Kandlakoya (V), Medchal Road, Hyderabad – 501401
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ENGINEERING PHYSICS LAB
GENERAL INSTRUCTIONS
1. Come to the Physics practical class with your observation book and completed record book.
2. Read the instructions for the experiment to be performed in advance and prepare for the practical before to the lab.
3. The procedure will be explained in the lab .and the student has to complete the experiment in time.
4. Know your apparatus and experimental arrangement.
5. Do not misuse the apparatus and take care of it.
6. Understand the experiment, complete it in all respects and take signature of the concerned faculty.
7. The doubts & difficulties, if any, should be discussed with the concern staff immediately.
8. Complete the required number of experiments (12) and maintain good record book to get more marks in practicals.
Experiment No. 1.
DETERMINATION OF RIGIDITY MODULUS OF THE MATERIAL OF A WIRE (Torsional pendulum)
AIM:- To determine the rigidity modulus ( ) of the given wire using Torsional pendulum.
APPARATUS:- Torsional pendulum, stop watch, meter scale, and vertical pointer clamp.
THEORY:-
A torsional pendulum is a flat disk, suspended horizontally by a wire attached at the top of the fixed support. When the disk is tuned through a small angle, the wire is twisted. On being released the disk performs torsional oscillations about the axis performs torsional oscillations about the axis of the support. The twist wire will exert a torque on the disk tending to return it to the original position. This is restoring torque. For small twist the restoring torque is found to be proportional to the amount of twist, or the displacement, so that
Ʈ = -kθ --------------à (1)
Here k is proportionality constant that depends on the properties of the wire is called torsional constant.
The minus sign shows that the torque is directly opposite to the angular displacement θ. Eqn. (1) is the condition for angular simple harmonic motion.
The equation of motion for such a system is
Ʈ = I α = I * d2θ/dt2 --------------à (2)
So that, on using the equation (1) we get
-kθ = I * d2θ/dt2
d2θ k
--- + ----- ( θ ) =0 --------------à (3)
dt2 I
The solution of the equation 3 is, therefore, a simple harmonic oscillation in the angle co-ordinate , namely
θ = θm cos(ωt+δ)
Here θm is the maximum angular displacement i.e. the amplitude of the angular oscillation
The period of oscillation is given by
Where I = rotational mertia of the pendulum & k = torsional constant
If k and I are known, T can be calculated.
PROCEDURE:-
Torsional pendulum consists of a uniform circular metal (brass or iron) disc of diameter about 10 cm and thickness of 1 cm. Suspended by a metal wire (whose n is to be determined) at the center of the disc. The other end of the wire is griped in to another chuck, which is fixed to a wall bracket. The length (l) of the wire between the two chucks can be adjusted and measured using meter scale. An ink mark is made on the curved edge of the disc. A vertical pointer is kept in front of the disc such that the pointer screens the mark when straight. The disc is set in to oscillations in the horizontal plane, by tuning through a small angle. Now stopwatch is started and time (t) for 20 oscillations is noted.
This procedure is repeated for two times and the average value is taken. The time period T (=t/20) is calculated.
The experiment is performed for five different lengths of
the wire and observations are tabulated in table.
The diameter and hence the radius (a) of the wire is
determined accurately at least at five different places
of the wire using screwguage since the radius of the
wire is small in magnitude and appears with forth power
in the formula of rigidity modulus
The mass (M) and the radius (R) of the circular disc are
determined by using rough balance and vernier respectively.
A graph is drawing between “ l “ on x-axis and T2 on y-axis
Rigidity modulus (n) of given wire is determine using the formula
η = 4π MR2 [l / T2] dyne/cm2
a4
OBSERVATION TABLE :-
Mass of the disc M = 970 gms
Radius of the disc R = gms
Radius of the wire, a
| S.No | PSR | HSR | L.C | PSR + (HSR*LC) | Diameter (cm) | Radius, a (cm) |
| | | | | | | |
| S. No | Length of the wire ‘l’ between chucks (cm) | Time taken for 20 Oscillations (sec) | Time Period T (sec) | T2 Sec2 | | ||
| Trial | Trial II | Mean | |||||
| | | | | | | | |
RESULT:-
Rigidity modulus of given wire is =----------------------------dynes/cm2
Experiment No. 2
STUDY OF NORMAL MODES ON A STRING USING FORCED VIBRATIONS IN RODS
(MELDE’S APPARATUS)
AIM:- To determine the frequency of a vibrating bar, or tuning fork using Melde’s arrangement.
APPARATUS:- Smooth pulley fixed to a stand, tuning fork, Connecting wires, Weight box, Pan Thread & Power supply.
THEORY:-
(a) Transverse arrangement:- The fork is placed in the transverse vibrations position and by adjusting the length of the string and weights in the pan, the string starts vibrating & forms many well defined loops. This is due to the stationary vibrations set up as results of the superposition of the progressive waveform the prong and the reflected wave from the pulley. Well-defined loops are formed when the frequency of each segment coincides with the frequency of the fork. The frequency n of the transverse vibrations of the stretched string by the tension of T dynes is given by:
Where m = mass per unit length of the string, l = length of a single loop.
Figure. The Envelope of standing waves
(b) Longitudinal arrangement:- When the fork is placed in the longitudinal position and the string makes longitudinal vibrations, the frequency of the stretched string will be half of the frequency (n)of the tuning fork, That is, when well-defined loops are formed on the string, the frequency of each vibrating segment of the string is exactly half the frequency of the fork.
During longitudinal vibrations, when the prong is in its right extreme position the string corresponding to a loop gets slackened string moves upto its initial horizontal position & becomes light. But when the prong is again in its right extreme position, thereby completing one vibration, the string goes up; its interia carrying it onwards and thereby completes only a half vibration.
Hence, the frequency of each loop is:
Where m = mass per unit length of the string, l = length of a single loop.
PROCEDURE:-
The apparatus (tuning fork) is first arranged for transverse vibrations, with the length of the string 3 or 4 meters & passing over the pulley. The circuit is closed vary the pot till the fork vibrates steadily. The load in the pan is adjusted slowly, till a convenient number of loops (say between 4 and 10) with well-defined nodes & maximum amplitude at the antinodes are formed, the vibrations of the string being in the vertical plane.
The number of loops (X) formed in the string between the pulley and the fork are noted. The length of the string between the pulley and the fork (d) is noted. The length (l) of a single loop is calculated by:
Let: m = mass of the pan, M = load added into pan.
Tension, T = (M + m)g dynes
Where g = acceleration due to gravity at the place.
The experiment is repeated by increasing or decreasing the load M, so that number of loops increases or decrease by one. The experiment is repeated till the whole string vibrates in one or loops & the observations are recorded.
Next the tuning fork is arranged for the longitudinal vibrations. The experiment is repeated as was done for the longitudinal vibrations & the observations are recorded.
At the end of the experiment, the mass m of the pan, the mass of the string (w) and the length (Y) of the strings are noted.
OBSERVATIONS:-
1. Mass of the string (thread) = W = …………gm (correct to a gm)
2. Length of the (thread) string = Y =………..cm
3. Linear density of the thread = (W/Y) =………..gm/cm
4. Mass of the pan = m = 7.54 gm (correct to a mg)
TABULAR COLUMN:-
For transverse arrangement
S.No. | Load applied in to the pan M gm | Tension T= (M+m)g dynes | No. of loops “X” | Length of ‘X’ loops=d cm | Length of each loop l=d/x cm | | |
| | | | | | | | |
For Longitudinal arrangement
S.No. | Load applied in to the pan M gm | Tension T= (M+m)g dynes | No. of loops “X” | Length of ‘X’ loops=d cm | Length of each loop l=d/x cm | | |
| | | | | | | | |
RESULT:-
1) Frequency of the tuning fork in Transverse mode n= _________ Hz
2) Frequency of the tuning fork in Longitudinal mode n= _____________Hz
Experiment No. 3
STUDY OF MAGNETIC FIELD ALONG THE AXIS OF A CIRCULAR COIL
(STEWART AND GEE’S METHOD)
AIM:- To study the variation of magnetic field along of a circular coil carrying current.
APPARATUS: Stewart and Gees type of tangent galvanometer, Rheostat, Ammeter, Deflection Magnetometer, Battery eliminator, commutator.
THEORY: The magnetic field (B) at a point on the axis of a circular coil carrying current “i” is given by the expression
monia2
B = -------------- Tesla.
2(x2+a2)3/2
Where ‘n’ is the number of turns, “a” the mean radius of the coil and “x” is the distance of the point from the center of the coil along the axis. To measure this field the Stewart and Gees type of tangent galvanometer is convenient.
The apparatus consists of a circular frame “c” made up of non-magnetic substance. An insulated Copper wire is wounded on the frame. The ends of the wire are connected to the other two terminals. By selecting a pair of terminals the number of turns used can be changed. The frame is fixed to a long base B at the middle in a vertical plane along the breadth side. The base has leveling screws. A rectangular non-magnetic metal frame is supported on the uprights. The plane of the frame contains the axis of the coil and this frame is supported on a movable platform. This platform can be moved on the frame along the axis of the coil. The compass is so arranged that the center of the magnetic needle always lie on the axis of the coil.
The apparatus is arranged so that the plane of coil is in the magnetic meridian. The frame with compass is kept at the center of the coil and the base is rotated so that the plane of the coil is parallel to the magnetic needle in the compass. The compass is rotated so that the aluminum pointer reads . Now the rectangular frame is along East-West directions. When a current “i” flows through the coil the magnetic field produced is in the perpendicular direction to the plane of the coil. The magnetic needle in the compass is under the influence of two magnetic fields. “B” due to coil carrying current and the earth’s magnetic fields “Be” which are mutually perpendicular. The needle deflects through an angle q satisfying the tangent law.
B= Be Tanq
The theoretical value of B is given by
monia2
B = -------------- Tesla.
2(x2+a2)3/2
PROCEDURE:- With the help of the deflection magnetometer and a chalk. A long line of about one meter is drawn on the working table, to represent the magnetic meridian. Another line perpendicular to the line is also drawn. The Stewart and Gees galvanometer is set with its coil in the magnetic meridian as shown in the fig. The external circuit is connected as shown in the fig. keeping the ammeter, rheostat away from the deflection magnetometer. This precaution is very much required because, the magnetic fields produced by the current passing through the rheostat and the permanent magnetic fields due to the magnet inside the ammeter affect the magnetometer reading, if they are close to it.
The magnetometer is set at the center of the coil and rotated to make the aluminum pointer reads, (0, 0) in the magnetometer. The key K, is closed and the adjusted so as the deflection in the magnetometer is about 600. The current in the magnetometer before and after reversal of current should not differ much. In case of sufficient difference say above 20 or 30 necessary adjustments are to be made.
The deflections before and after reversal of current are noted when d = 0. The readings are noted in Table 1.The magnetometer is moved towards East along in steps of 5cm at a time. At each position, the key is closed and the deflections before and after reversal of current are noted. The mean deflection be denoted as qE The magnetometer is further moved towards east in steps of 5cm each time and the deflections before and after reversal of current be noted, until the deflection falls to 300 .
The experiment is repeated by shifting the magnetometer towards West from the center of the coil in steps of 2 cm, each time and deflections are noted before and after reversal of current. The mean deflection is denoted as qW.
It will be found that for each distance (x) the value in the last two columns of the second table are found equal verifying equation (1) & (2).
A graph is drawn between x (the distance of the deflection magnetometer from the center of the coil) along x=axis and the corresponding TanqE and TanqW along Y-axis. The shape of the curve is shown in the fig. The point A and B marked on the curve lie at distance equal to half of radius of the coil (a/2) on either side of the coil.
CIRCUIT DIAGRAM:-
MODEL GRAPH:-
OBSERVATION TABLE:-
Horizontal component of earth’s magnetic field Be = 0.38 X 10 -4 Tesla ( or Wb . m-2)
Radius of coil (a)= meter (diameter of coil /2)
Current carrying in the ammeter= Amp
m0 = 4p X 10-7
| Distance From the Center of coil | Deflection in East direction | Mean qE | Deflection in West direction | Mean qW | qE+qW q = ----------- 2 | Tanq | ||||||
| q1 | q2 | q3 | q4 | q1 | q2 | q3 | q4 | |||||
| | | | | | | | | | | | | |
| Distance X in meter | Theoretical B | Practical B |
| | | |
RESULT:-
Verified the magnetic field along the current carrying coils at different places Theoretically & practically and they are same.
Experiment No. 4
DISPERSION OF LIGHT
{Prism – Spectrometer method}
AIM: - To determine the dispersive power of the material of the given prism by the spectrometer.
APPARATUS :- Spectrometer ,Mercury Vapour Lamp & Prism
THEORY :- The essential parts of the spectrometer are:(a) The telescope, ( b)
The collimator & (c) prism table.
( a ) The Telescope :-
The telescope is an astronomical type .At one end of a brass tube is an objective, at the other end a (Rams den’s) eye piece and in between , a cross wire screen .The eye piece may be focused on the cross –wires and the length of the telescope may be adjusted by means of a rack and pinion screw .The telescope is attached to a circular disc ,which rotates symmetrically about a vertical axis and carries a main scale , divided in half – degrees along its edges. The telescope may be fixed in any desired position by means of a screw &fine adjustments made by a tangential screw
( b )The Collimator : -
The collimator consists of a convex lens fitted at one end of a brass tube and an adjustable slit at the other end . The distance between the two may be adjusted by means of a rack and pinion screw .The collimator is rigidly attached to the base of the instrument .
( c ) The prism Table : -
The prism table consists of a two circular brass discs with three leveling screws between them. A short vertical brass rod is attached to the center of the lower disc & this is fitted into a tube attached to another circular disc moving above the main scale. The prism table may be fixed on the tube by means of a screw. The second circular disc moving over the main scale carries two verniers at diametrically opposite. The vernier disc also revolves about the vertical axis passing through the center of the main scale and may be fixed in any position with the help of a screw .A tangential screw is provided for fine movements of the vernier scale.
Most Spectrometers have 29 main scale divisions ( half –degrees ) divided on the vernier into thirty equal parts .Hence , the least count of the vernier is one – sixteenth of a degree or one minute .
Preliminary Adjustments : -
The following adjustments are to be made before the commencement of an experiment with spectrometer.
( i ) Eyepiece Adjustment : -
The telescope is turned towards a bright object, say a white wall about 2 to 3 meters way and the eyepiece is adjusted so that cross - wires are very clearly seen. This ensures that whenever an image is clearly seen on the cross – wires, the eye is an unstrained condition.
( ii ) Telescope Adjustment : -
The telescope is now turned towards a bright object, and its length is adjusted until the distant objects is clearly seen in the plane of the cross – wires: that is the image suffers no lateral displacement, with the cross – wire of the eye shifted slightly to and fro. In this position the telescope is capable of receiving parallel rays. This means that whenever any image is seen clearly on the cross – wires, it may be taken that the rays entering the telescope constitute a parallel bundle.
In case the experiment is to be performed in a dark room from which a view of distant object is difficult to obtain, the method suggested by Schewster may be adopted.
A prism is placed on the prism table and a refracted image of the slit is viewed .The prism is adjusted to be almost at minimum deviation .At this stage, it will be found that the image is fixed telescope for two positions of the prism ,which may be obtained by turning the prism table one way or other. The prism table alone is adjusted so that the image leaves the field of vision (traveling towards the direct ray) and returns again. Now the collimator alone is adjusted for clarity of image. This is repeated a few times until the image is quite clear.
( iii ) collimator adjustment : -
The slit of collimator is illuminated with light. The telescope is turned to view the image of the slit and the collimator screws are adjusted such that a clear image of the slit is obtained without parallax in the plane of the cross – wires. The slit of the collimator is also adjusted to the vertical & narrow.
The refractive index of the material of the prism is given by
Sin(A+D/2)
m = ------------------ ------------------------- (1)
Sin(A/2)
Where A is the angle of the equilateral prism and D is the angle of minimum deviation
When the angle of incidence is small, the angle of deviation is large .As the angle incidence is slowly increased, the angle of deviation begins to diminish progressively , till for one particular value of the angle of incidence , the angle of deviation attains a least value . This angle is known as the angle of minimum deviation D
The dispersive power (ω) of the material of the prism is given by
m B -mR
ω = ---------- --------------------- (2)
(m-1)
Where m B = the refractive index of the blue rays
m R = the refractive index of the red ray and
(m B + mR)
m = -------------- ; the mean of m B and m R
2
Noting the angle of minimum deviation D . for blue & red rays m B and m R are calculated using equation (1 ) and using equation ( 2 ) the dispersive power of the material of the prism is calculated .
PROCEDURE: -
The prism is placed on the prism table with the ground surface of the prism on to the left or right side of the collimator. Care is to be taken to see that the ground surface of the prism does not face either the collimator or the telescope. The vernier table is then fixed with the help of vernier screw.
The ray of light passing through the collimator strikes the polished surface BC of the prism at Q and undergoes deviation along QR and emerges out of the prism from the face AC. The deviated ray (continuous spectrum) is seen through the telescope in position T2. Looking at the spectrum the prism table is now slowly moved on to the one side, so that the spectrum moves towards undeviated path of the beam. The deviated ray (spectrum) also moves on to the same side for some time and then the ray starts turning back even though the prism table is moved in the same direction. The point at which the ray starts turning back is called minimum deviation position. In the spectrum, it is sufficient if one colour is adjusted for minimum deviation position. In this limiting position of the spectrum, deviation is minimum. The telescope is now fixed on the blue colour and the tangent screw is slowly operated until the point of intersection of the cross wire is exactly on the image. The reading for the blue colour is noted in vernier I and vernier II and tabulated. The reading is called the minimum deviation reading for the blue colour. The telescope is now moved on the red colour and the readings are taken as explained for blue colour.
Next, the telescope is released and the prism is removed from the prism table. The telescope is now focused on to the direct ray (undeviated path) and the reading in vernier I and vernier II are noted.
The difference of readings between the deviated reading for blue colour and the direct reading gives the θ angle of minimum deviation, reading for the blue colour (DB). Similarly, the difference of readings between the deviated reading for the red colour and the direct reading gives the angle of minimum deviation for the red colour (DR). the refractive indices for the blue and red rays are calculated using equation (1) (Assuming the angle of the equilateral prism, A = 60O , the values of m B and m R
are substituted in equation (2) and the dispersive power of the material of the prism is calculated.
CIRCUIT DIAGRAM:-
Arrangement of prism for dispersive power
OBSERVATION TABLE:-
Least count of the vernier of the spectrometer, LC=
Angle of prism A=
Direct reading Vernier I =
Vernier II =
| Colour of the line | Position of minimum deviation | Angle of minimum deviation | ||
| Vernier I | Vernier II | Vernier I | Vernier II | |
| | | | | |
| Blue Red | | | | |
RESULT:-
Dispersive power of the given material of the prism is = --------------
Experiment No. 5
DIFFRACTION GRATING
(NORMAL INCIDENCE & MINIMUM DEVIATION)
AIM : - To determine the wavelength of a given light radiation using diffraction grating with (a ) Normal incidence and ( b ) Minimum deviation method .
APPARATUS:- Spectrometer , Sodium , vapour Lamp & Grating
DESCRIPTION:-
A plane diffraction grating consists of a parallel – sided glass plate with equidistant parallel lines drawn very closely on it by means of a diamond point 15,000 lines per inch or (15,000/25.u) lines per cm are drawn on the grating. Such gratings are known as original gratings. But the gratings used in the fixed over as optically plane glass plane. Care should be taken while handling the grating. It should be handled by the edge of the plate.
THEORY:-
A parallel beam of monochromatic light from the collimator of a spectrometer is made to fall normally on a plane diffraction grating erected vertically on the prism table .The telescope initially in line with the collimator is slowly turned to one side. A line spectrum will be noticed and on further turning the telescope the line spectrum will again be noticed. While the former is called the first order spectrum, the later is called the second order spectrum .On further rotating the telescope .the third order spectrum may also be noticed, depending on the quality of the grating. But the number of orders of spectra that can be observed with a grating limited. With the light normally incident on a grating having N lines per cm. if θ is the angle of diffraction of a radiation of wavelength λ in the nth order spectrum then
n λ N = Sin θ
Sin θ
or λ = --------
nN
Sin θ X 2.54
or λ = ---------------- ------------------- (1)
n X 15,000
Knowing θ and n, the wavelength of light radiation is calculated using equation (1) for the normal incidence method.
Again when a parallel beam of monochromatic light is incident upon a grating is diffracted in such a way that the angle of deviation is minimum; then the wavelength (λ) Of the radiation is given by
2 Sin (D/2)
λ = ----------------
Nn
2 X 2.54 X Sin (D/2)
λ = -------------------------- ------------------- (2)
15,000
Where D is the angle of minimum deviation and “ n “ is the order of spectrum. Equation (2) is used for the minimum deviation to calculate the wavelength of the light radiation .
PROCEDURE:-
a. Normal incidence method: - preliminary adjustments of the spectrometer are made. Focusing and adjusting the eye piece of the telescope to a distant object. The grating table is leveled with a spirit level .The grating is mounted on the grating table for the normal incidence .The slit of collimator is illuminated with sodium light .
The direct reading is taken the telescope is turned from the position through 90o and fixed in this position, as shown in the fig -1
The grating is mounted vertically on the grating platform the rulings on it being parallel to the slit in the collimator. The platform is now rotated until the image of the slit as reflected by the glass surface is seen in the telescope. The vertically cross wire is made to coincide with the fixed edge of the image .The platform is fixed in this position, The vernier table is now rotated in the appropriate direction through 45o so that the rays of light from the collimator fall normally, on the grating
Grating set for normal incident light
The telescope is now released and rotated it so as to catch the first order – diffracted image on one side, say right (or left) as shown in the fig 2.with sodium light two images of the slit, very close to each other are seen. These are the D and D lines of sodium light .The point of intersection of the cross wires is set on the D line and the reading in the vernier I &II is noted. Similarly, the reading corresponding to the D line is noted .the telescope is now focused to the direct ray passing through the grating and the point of intersection of the crosswire is set on the direct ray .The reading in the vernier I &II is noted. The difference in the readings corresponding to any one gives the angle of diffraction θ for that line in the first order spectrum.
Diffracted image
Tabular column:-
| S.No | Spectral Line | Wavelength in A0 | Position of Telescope | | Sinq | |||||
| Left Side qL(degree minutes) | Right side qR(degree minutes) | |||||||||
| Main | Vernier | Total | Main | Vernier | Total | |||||
| 1st | D1 | | | | | | | | | |
| | D2 | | | | | | | | | |
| 2nd | D1 | | | | | | | | | |
| | D2 | | | | | | | | | |
RESULT:-
Wavelength of the given light source is =
Experiment No. 6
NEWTON’S RINGS
AIM:- To determine (a ) the wavelength of sodium vapour light /or (b) the radius of curvature of the surface of the lens , by forming Newton’s rings
APPARATUS:- Newton’s ring set & plane mirror .
THEORY:-
Let R = Radius of curvature of the surface of the lens In conduct with the glass plate (P1)
D1=Diameter of the n1th ring
D2= Diameter of the n2th ring
Then, the relation gives the wavelength of the light radiation:
(D22-D12)
= --------------- -------------------- (1)
4R(n2-n1)
The radius of curvature of the lens is determined with a spectrometer. The values of D1 and D2are very small and occur to the second power in equation (1). Hence they are to be measured carefully with the traveling microscope. Care is to be taken in moving the microscope to travel in a direction without moving back and forth while taking readings. This is very essential since the variation in the diameter of the rings is in the second decimal place and any back and forth movement of the microscope will result in wrong readings .it can be seen from equation (1) that the diameter of the rings increase with the increase in the radius of curvature R of the lens .With a lens of radius of curvature of about 100 cm, the rings formed will be convenient for measurement .Hence ,it is desirable to select a Plano convex lens of long focal length for forming rings .
PROCEDURE:-
The apparatus consists of a light source . The light from it is rendered parallel by means of a convex lens. The parallel rays are incident on a plane glass plate through the magnifying glass inclined at 45o to the path of incident rays. Alternate bright & dark rings are observed through a traveling microscope.
The point of intersection of cross wires in the microscope is brought to the center of ring system, if necessary, tuning the cross wires such that one of them is perpendicular to the line of travel of the microscope. The wire may be set tangential to any one ring; & starting from the center of the ring system, the microscope is moved on to one side, say left, across the field of view counting the number of rings. After passing beyond 25th ring, the direction of motion of the microscope is reversed and the cross wire is set at the 20th dark ring, tangential to it. The reading on the microscope scale is noted. Similarly, the readings with the cross-wires set on 18th, 16th, 14th,………2nd dark rings are noted. The microscope is moved in the same direction and the readings corresponding to the 2nd, 4th, 6th………. dark ring on the right side are noted. Readings are to be taken with the microscope moving in one & the same direction to avoid errors due to backlash The observations are recorded in table 1.
The Plano convex lens is taken out from the traveling microscope and the radius of curvature is determined by a spherometer.
A graph is drawn with the number of rings as abscissa (X-axis) and the square of diameter of the ring as ordinate (Y-axis). The nature of the graph will be straight line as shown in the fig. From graph the values of D12 and D22 corresponding to two number n1 and n2 are noted. Using these values in equation (1) the wavelength of the source λ is calculated.
To determine the radius of curvature, R, of the lens; the wavelength, λ of the source used is to be taken standard tables.
CIRCUIT DIAGRAM:-
Arrangement of Newton’s Ring
OBSERVATIONS:- Radius of curvature of the lens in contact with glass R = cm.
TABULAR COLUMN:-
| S.No | Ring Number | Microscope Reading Left side L1 Right side R1 | Diameter of nth ring D=(L1 ~ R1) | Square of diameter of the ring. D2 |
| | | | | |
RESULT:-
Wavelength of the given light source is = --------------------
Experiment No. 7
DETERMINATION OF LASER RADIATION
AIM:- To determine the wave length of a given source of Semiconductor laser using a plane transmission grating by normal incident method.
APPARATUS:- Plane diffraction grating, laser beam of Semiconductor source, a scale and prism table.
THEORY:-
An arrangement consisting of large number of parallel slits of the same width (e) and separated by equal opaque space (d) is known as the “diffraction grating ” (e+d) is known as the grating element. A grating is constructed by rubbing equidistant parallel lines ‘N’ ruled on the grating per inch are written over it.
Hence (e+d) = l ”= 2.54 cm
i.e. the grating element (e+d)= 2.54 cm.
The normal critical incidence the condition for obtaining principle maxima is-
(e+d) sinθ = + λ
Where λ is wavelength of light
N Lines per inch on the plane diffraction grating
And n is order of diffraction light.
PROCEDURE:-
Keep the grating in front of the laser beam such that light is incident normally on it. When light of laser falls on the grating the central maxima along with four other lights are seen on the screen. The light next to central maxima and light next to first order is second order maxima.
Now measure the distance between the grating and the screen and tabulate it as “d1” and the distance between central maxima to first order and then central maxima and second order is “d2”and it is also tabulated.
OBSERVATION TABLE:-
Number of lines on the grating N=
The distance between grating and the screen D= cm
| Order No | Left side d1 | Right side d2 | Mean d | | λ = Sin θ/nN |
| | | | | | |
PRECAUTIONS:-
1) Do not look at the laser beam directly.
2) The prism table should be perpendicular to the laser and laser beam and the grating should be horizontal.
RESULT:-
The wave length of Semiconductor laser beam= nm.
Experiment No. 8
ENERGY GAP OF A SEMI CONDUCTOR
AIM: - To determine the energy gap of a semiconductor diode.
APPARATUS:- Germanium diode (OA 79), Thermometer, Copper Vessel, Regulated DC power supply, Micro ammeter, Heater & Bakelite lid.
PROCEDURE:- Connections are made as per the circuit diagram. Pour some oil in the copper vessel. Fix the diode to the bakelite lid such that it is reversed biased. Bakelite lid is fixed to the copper vessel, a hole is provided on the lid such that it is reversed biased. Bakelite lid is fixed to the copper vessel, a hole is provided on the lid through which the thermometer is inserted into the vessel. With the help of heater, heat the copper vessel till temperature reaches upto 80oC. Note the current reading at 80oC apply suitable voltage say 1.5v (which is kept constant) & note the corresponding current with every 5oC fall of temperature, till the temperature reaches the room temperature.
A graph is plotted between l /T (K) on x-axis and log 10 R on y-axis is a straight line. Slope is measured by taking the values of two points where each one of them intersects on the straight line as shown in the fig.
The energy gap = slope x Boltzmann’s constant / log 10 e.
The energy gap Eg = 1.9833 X slope X 10-4 ev
NOTE:- Do not allow the temperature to rise 100oC if you switch off the heater at
80oC it will keep on rising for few minutes and may go upto 85/90 degress before stabilizing/falling.
CIRCUIT DIAGRAM:-
· Depending upon the doping level of the diode the energy gap may vary between 0.5ev to 0.7ev.
TABULAR FORMAT:-
V= 1.5 Volt
| Temperature t Co | T= t + 273 K | Current I μA | R=V/I Ω | Log10R | 1 / T K-1 |
| | | | | | |
RESULT:-
Energy gap of the given semiconductor is ---------------------eV
Experiment No. 9
RC CIRCUIT
AIM:- To study the decay of current in a RC circuit and to determine RC time constant.
APPARATUS:- Fixed Power supply, Switch, Ammeter, Combinations of Resistor & Capacitors.
THEORY:- When a condenser ‘C’ is charged through a resistance ‘R’ then charge increases exponentially in accordance with the formula.
Q = Qo (1-e t/RC)
Where Q is the charge in time t; and
Qo is the maximum charge.
The product ‘CR’ is called time constant. It is the time taken to establish ( l – e ) part of the maximum charge in the condenser. It is equal to the time taken to establish 0.632 part of the total charge.
When a condenser is discharged through a resistance, the charge falls in accordance with the formula.
Q = Qo e –t/RC
The time constant in this case is equal to the time, taken to decrease the charge of ‘e’ part of the maximum charge. It is equal to the time taken to discharge to a value of 0.368 part of maximum charge.
i.e. we can say that I = dq / dt
= -to e-t/RC
Where C = capacitor in farad R = resistance in ohm I = current in the circuit
When I = 0.36 Io then t = RC
PROCEDURE:-
Rig up the circuit as per the circuit diagram. Clinching Flip the switch towards push to charge, the capacitor start charging towards the power supply. The switch is in this position for short interval of time until the ammeter shows maximum deflection, but within the limit. Note down the maximum current as Io. Now flip the switch to other side and start the stop clock. The current start falling. Note the ammeter reading at a regular time interval.
Plot the graph of current (l) on Y-axis and time (t) on X-axis.
CIRCUIT DIAGRAM:-
OBSERVATION TABLE:-
C1 = farad, C2 = farad & C3 = farad.
| S.No | Voltage volts | Time in sec | ||
| For R = Ω | ||||
| C1 | C2 | C3 | ||
| | | | | |
GRAPH:-
Draw an intercept to the X-axis as shown in the graph the corresponding t gives the time constant.
RESULT:-
Time constant of RC circuit is------------sec
Experiment No. 11
LOSSES IN OPTICAL FIBERS
Aim:- To study various types of losses that occur in optical fibers and measure losses in dB of two optical fiber patch cords at two wavelengths , namely ,660nm and 850nm. The coefficients of attenuation per meter at these wavelengths are to be computed from the results.
Basic Definitions
Attenuation in an optical fiber is a result of a number of effects .We will confine our study to measurement of attenuation in two cables (cable 1 and cable 2)employing an SMA –SMA in -line – adapter .We will also compute loss per meter of fiber in dB. We will also study the spectral response of the fiber at 2 wavelengths ,660nm and 850nm
The optical power at a distance ,L, in an optical fiber is given by where Po is the launched power and is the attenuation coefficient in decibels per unit length .The typical attenuation coefficient value for the fiber under consideration here is 0.3dB per meter at a wavelength of 660nm .Loss in fibers expressed in decibels is given by –10log (Po/Pf) where, Po is the launched power and Pf is power at the far end of the fiber. Typical losses at connector junctions may vary from 0.3 dB to 0.6 dB.
Losses in fibers occur at fiber-fiber joints or splices due to axial displacement, angular displacement, separation (aircore), mismatch of cores diameters, mismatch of cores diameters, mismatch of numerical apertures, improper cleaving and cleaning at the ends. The loss equation for a simple Fibre-optic link is given as:
Pin (dBm)-Pout (dBm)= LJ1+LFIB1+LJ2+LFIB2+LJ3 (JB): where, L J1 (dB) is the loss at the LED-connector junction, L FIB1 (dB) is the loss in cable1, LJ2 (dB) is the insertion loss at a splice or in-line adapter, L FIB2 (dB) is the loss in cable2 and LJ3 (dB) is the loss at the connector-detector juntion.
Procedure with Block Schematic
The schematic diagram of the optical fiber loss measurement system is shown below and is self explanatory.
Step1: Connect one end of Cable 1 to the LED1 port of the PHY 148-TX and the other end to the FO PIN port (powermeter) of PHY – 149-RX unit.
Step2: Set the DMM to the 2000 mV range. Turn the DMM on. The powermeter is now ready for use.
Step3: Plug the AC mains for both units. Connect the optical fiber Patchcord, Cable1 securely, as shown, after relieving all twists and strains on the fiber.While connecting the cable please note that minimum force should be applied. At the same time ensure that the connector is not loosely coupled to the receptable. After connecting the optical fiber cable properly, adjust SET Po knob to set power of LED1 to a suitable value, say, -15.0dBm (the DMM will read 150 mV). Note this as Po1
Step4: Wind one turn of the fiber on the mandrel, as shown in Experiment 1 and note the new reading of the powermeter Po2. Now the loss due to bending and strain on the plastic fiber is Po1-Po2 dB. For more accurate readout set the DMM to the 200.0mV range and take the measurement. Typically the loss due to the strain and bending the fiber is 0.3 to 0.8 dB.
Step5: Next remove the mandrel and relieve Cable1 of all twists and strains. Note the reading Po1. Repeat the measurement with Cable2 (5 meters) and note the reading Po2. Use the in-line SMA adaptor and connect the two cables in series as shown. Note the measurement Po3.
Loss in Cable1=Po3-P02- Lila Loss in Cable 2=Po3-Po1-Lila
Assuming a loss of 1.0dB in the in-line adapter (Lila=1.0dB), we obtain the loss in each cable. The difference in the losses in the two cables will be equal to the loss in 4 meters of fiber (assuming that the losses at connector junctions are the same for both the cables). The experiment may be repeated in the higher sensitivity range of 200.0mV. The experiment also may be repeated for other Po settings such as-15dBm, -20 dBm, -25dBm etc.
Table of Readings for 660nm,
| Sl No | Po1 (dBm) | Po2 (dBm) | Po3 (dBm) | Loss in Cable1 (dB) | Loss in Cable2 (dB) | Loss in 4 meters fider (dB) | Loss per meter (dB) at 660nm |
| 1 | -15.0 | | | | | | |
| 2 | -20.0 | | | | | | |
| 3 | -25.0 | | | | | | |
| 4 | | | | | | | |
Step6: Repeat the entire experiment with LED2 at 850nm and tabulate
NOTE
The power meter has been calibrated internally to read power in dBm at 660nm. However the calibration has to be redone manually for measurements at 850nm. The PIN has a 66% higher sensitivity at 850nm as compared to 660nm for the same input optical power. This corresponds to sensitivity higher by 2.2dB. To calibrate the power meter at 850nm, deduct 2.2dB from the measured reading. In computing losses in cables and fibers this gets eliminated while solving the equations.
Table of Readings for 850nm,
| Sl No | Po1 (dBm) | Po2 (dBm) | Po3 (dBm) | Loss in Cable1 (dB) | Loss in Cable2 (dB) | Loss in 4 meters fider (dB) | Loss per meter (dB) at 8500nm |
| 1 | -15.0 | | | | | | |
| 2 | -20.0 | | | | | | |
| 3 | -25.0 | | | | | | |
| 4 | | | | | | | |
Inferences:
Due to differences in alignment at different connectors, in each of the removal and replacement operation, we experience variations in loss. The observed values will be closer to the true values, if we take the average of many readings. The attenuation coefficient of aprrox 0.3dB per meter at 660nm is normally well defined, as per the specifications of the manufacturers. Deviation, if any, will be due to connector losses not being identical for the two cables. Also the assumed value of lose in the In-line-adapter (1.0dB) may be off the mark in some cases.
The loss per meter of cable at 850nm is not specified by the manufacturers. The range of loss 2.5dB+/-1.0 dB is acceptable.
RESULT:-
Bending loss of the given optical fibre is -------------- dB
Experiment No. 12
NUMERICAL APERTURE
AIM: To determine the numerical aperture (NA) of the given optical fiber.
APPARATUS: One or two meters of the step index fiber, Fiber optics kit, and scale.
THEORY:
The numerical aperture of an optical system is the light gathering capacity, which is a measure of the light collector by an optical system. It is the product of the refractive index of incident medium and the size of maximum ray angle, which is called acceptance angle.
NA = n1 sinq max
For air nI =1
NA = n1 sinq max
Light from fiber end a falls on the screen BC. Let the diameter of the light falling on the screen = BC = d
Let the distance between the fiber end and the screen is AO = b
From geometry
AO = b
.’. AC = Ö(b2+r2)
Sinq =OB / AB = (b2+r2)
From the above equation the NA can be calculated.
B
| LED |
O W
A
D
L
PROCEDURE:
- The twists or microbends on the fiber if any are to be removed
- One end of the fiber is connected to the transmiter.
- The AC main is switched on and the light passing through the cable from one end is collected at the other end of the fiber is observed to ensure that the coupling is made or not
- The set p0 knob is turned to get maximum intensity of light through fiber.
- The fiber is kept at a height (say – 1cm) from the paper so that light falls on the paper in circular shape (output).
- Draw a circle with the dimensions of the light coming out of the fiber on the paper
- Measure the radius of the circle, Let it be ‘r’
- Repeat the experiment with different heights and find different ‘r’.
- Tabulate the readings.
- The NA can be calculated with the formula NA = sinq max
Tabular column:-
| S.No | L(mm) | W(mm) | NA | (Degrees) |
| 1 | | | | |
| 2 | | | | |
| 3 | | | | |
| 4 | | | | |
| 5 | | | | |
RESULT:-
1) Numerical Aperture of given optical fibre is ----------------
2) Acceptance angle of given optical fibre is ----------------- degree
Experiment No. 13
L C R circuit
AIM: - To study the series and parallel resonance circuit and to find frequency and quality factor.
APPARATUS: -Set of resistors, Capacitors, Inductors and Milli ammeter.
R = 150 R = 150 R = 330
C = 0.01 μF C = 0.1 μ F C = 0.22 μ F
L = 2.5mH L = 5mH L = 7.5mH
PROCEDURE: -
SERIES RESONANCE: -
1. Connect the circuit as shown in the circuit diagram.
2. Apply input signal using signal generator. The output should be 10V only.
3. Take the output across the resistor and feed it to Ammeter input sockets.
4. Vary the frequency till the Ammeter records a sharp rise and fall, adjust the signal such that the Ammeter deflection is the maximum possible. This is the resonant frequency of
the connected combination of the circuit.
5. Adjust the signal generator amplitude such that to get full-scale deflection. In Ammeter now reduce the frequency till the deflection falls considerably. Then increase the frequency in regular intervals & note down the Ammeter readings.
6. Plot a graph between the meter deflection divisions and frequency.
7. Repeat the procedure using different combinations of L, C & R and study how Q is affected. Also study how Resonant Frequency depends upon different combination of L.C.R.
PARALLEL RESONANCE: -
1. Connect the circuit as per the circuit diagram.
2. Apply input signal, from a reliable signal generator. The output should be 10V only.
3. Take the output across the tank circuit and connect to Ammeter input sockets.
4. Vary the frequency till the Ammeter records sharp fall. Adjust the signal such that the deflection falls down considerably. Then increase the frequency in regular intervals and note down the deflection.
5. Adjust the signal generators amplitude such that, to get full-scale deflection. Now reduce the frequency till the deflection falls down considerably. Then increase the frequency in regular intervals & note down the deflection.
6. Plot graph between the meter deflection divisions and frequency.
7. Repeat the procedure for different values of R and study how Q is affected. Also study
how resonant frequency depends on different combinations of L.C.R.
CALCULATIONS: -
For series circuit Z is minimum at Resonance.
Resonance frequency of series circuit is-
Zo = R + Ro
Eo = RIo
Ro is the resistance of the coil.
(ω = f2 – f1)
is the point beyond the fo (at the point Eo/2)
f1 is the point before fo (at the point Eo/2)
For parallel circuit Z is maximum at resonance.
or Qo =L Wo
(ω = f2 – f1)
CIRCUIT DIAGRAM: -
1) LCR Series Circuit
2) LCR Parallel Circuit
Graph:-
Result:-
1. Resonance frequency in series circuit is ……………… Hz.
2. Resonance frequency in parallel circuit is ……………. Hz.
3. Resonance frequency theoretical value is …………….. Hz.
