ANURAG COLLEGE OF ENGINEERING (ANRH)

Aushapur(V), Ghatkesar(M), Medchal(Dist)- 501301

DEPARTMENT OF BASIC SCIENCES AND HUMANITIES

PH105BS : ENGINEERING PHYSICS LAB B.Tech. I Year I Sem

( Common for Civil, ME, AE, ME (M), MME, Mining & Petroleum Engg.)

List of Experiments:-

1. Melde’s experiment: To determine the frequency of a vibrating bar or turning fork using

Melde’s arrangement.

2. Torsional pendulum: To determine the rigidity modulus of the material of the given wire using

torsional pendulum.

3. Newton’s rings: To determine the radius of curvature of the lens by forming Newton’s rings.

4. Diffraction grating: To determine the number of lines per inch of the grating.

5. Dispersive power: To determine the dispersive power of prism by using spectrometer.

6. Coupled Oscillator: To determine the spring constant by single coupled oscillator.

7 .LCR Circuit: To determine quality factor and resonant frequency of LCR circuit.

8 LASER: To study the characteristics of LASER sources.

9. Optical fiber: To determine the bending losses of Optical fibers.

10. Optical fiber: To determine the Numerical aperture of a given fiber.

Fig :- A standing wave is created when an incident and reflected wave have identical amplitudes,

wavelengths and velocities.

Fig :- Transverse arrangement

Fig :- Longitudinal arrangement

MELDE’S EXPERIMENT-Transvers and Longitudinal Modes

AIM: -To determine the frequency of a vibrating bar of tuning fork using Melde’s arrangement in

transverse and longitudinal modes.

APPARATUS: -Smooth pulley fixed to a stand, tuning fork, Connecting wires, Weight box, Pan, Thread & Battery eliminator.

THEORY: -When a vibrating body produces waves along a tightly stretched string, the waves are reflected

at the end of the string, which cause two opposite traveling waves to exist on the string at the same time.

These two waves interfere with each other, creating both constructive and destructive interference in the

vibrating string. If the two waves have identical amplitudes, wavelengths and velocities, a standing wave or

stationary wave is created.

The constructive and destructive interference patterns caused by the superposition of the two waves

create points of minimum displacement called nodes, or nodal positions, and points of maximum

displacement called antinodes. If we define the distance between two nodes (or between two antinodes)

to be , then the wavelength of the standing wave is . Figure illustrates the case where the length

of string vibrates with 5 nodes and 4 antinodes. On the basis of the direction of movement of the individual

particles of the medium relative to the direction that the waves travel in Transverse and Longitudinal

modes.

a) Transverse arrangement: In this arrangement, a wave in which particles of the medium moves in a

direction, perpendicular to the direction of the propagation. The fork is placed in the transverse vibration

position and by adjusting the length of the string and weights in the pan, the s tr i ng starts vibrating &

f o rm s many wel l -defined l oops . The time, during which the tuning fork completes one vibration, the

string also completes one vibration. In this mode, frequency of the string is equal to the frequency of the

tuning fork.

b) Longitudinal arrangement: In this arrangement a wave in which particles of the medium move in a

direction parallel to the direction of the propagation. When the fork is placed in the longitudinal position

and the string makes longitudinal vibrations, The time, during which the tuning fork completes one

vibration, the string completes half of its vibration. In this mode, frequency of the fork is twice the frequency of the string. In longitudinal drive mode, since the string tension increases and decreases once per tuning

fork vibration, it takes one tuning fork vibration to move the string loop to maximum upward position and

one to move it to maximum downward position. This is two tuning fork vibrations for one upward and downward string vibration, so the tuning fork frequency is half the string frequency.

FORMULA :-

In Transverse arrangement frequency of the tuning fork

η1 = 1

2𝐿

√𝑇

√𝜇 Hz

In Longitudinal arrangement frequency of tuning fork η2 = 2 η1

Where µ = mass per unit length of the string(linear density)

L = length of a single loop

T = tension =(M+m) g

g = acceleration due to gravity

mass per unit length of the string µ= (W/Y) = --------gm/cm

Table: - 1

For transverse Mode:

S.no. Load applied

into the pan

(M) gm

Tention

T=(M+m)g

dynes

No. of

loops

“x”

Length of

‘x’

loops=d

cm

Lenth of

each loop

L=d/x cm

√𝑻

dynes

√𝑇

𝐿

dynes/cm

1.

2.

3.

4.

5.

Table: - 2

For longitudinal Mode:

S.no.

Load applied

into the pan

(M) gm

Tention

T=(M+m)g

dynes

No. of

loops

“x”

Length of

‘x’

loops=d

cm

Lenth of

each loop

L=d/x cm

√𝑻

dynes

√𝑇

𝐿

dynes/cm

1.

2.

3.

4.

5.

OBSERVATIONS: -

1. Mass of the string (thread) = W = -------gm

2. Length of the (thread) string = Y = -----cm

3. mass per unit length of the string µ= (W/Y) = --------gm/cm

4. Mass of the pan = m = --------gm

5. Accelelaration due to gravity = g = --------cm/s2

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 umber 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= d/x) of a single loop is calculated.

Increasing or decreasing the load M repeats the experiment, so that the number of loops increases or decreases by one. The experiment is repeated till the whole string vibrates in one or two 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

PRECAUTIONS:-

1. Pulley should be frictionless.

2. The thread should be thin, uniform and inextensible.

3. Weight of the scale pan should be added.

4. The loops formed in the thread should appear stationary.

5. Do not put too much load in the pan.

RESULT:-

Frequency of the tuning fork in transverse mode is --------------- Hz

Frequency of the tuning fork in longitudinal mode is ------------- Hz

Torsion Pendulum

Table:1

TO Determine the time period of torsional pendulum for 10 oscillations

S.No Length of the wire

‘l’ between chucks

(cm)

Time taken for 10 Oscillations

(sec)

time period

T=𝒕

𝟏𝟎

(sec)

T 2

(sec2)

𝒍

𝑻𝟐

(𝒄𝒎

𝒔𝒆𝒄𝟐) Trial I (t1)

( sec)

Trial II (t2)

(Sec)

Mean(t) t=𝒕𝟏+𝒕𝟐

𝟐

(sec)

1.

2.

3.

4.

5.

6.

TORSIONAL PENDULUM

AIM:

To determine the rigidity modulus (η) of the material of the given wire using torsional

pendulum.

APPARATUS:

Torsion pendulum, wire, Stop clock, meter scale, and vernier caliper, Screw Gauge,

Electrical balance

THEORY:

When the suspension wire is twisted by the circular disc fixed at the bottom of the wire, the wire

undergoes shearing strain. This is called torsion. Because of this torsion, the disc executes oscillations

called torsional oscillations. The angular acceleration of the disc is proportional to its angular

displacement and is always directed towards its mean position. Hence, the motion of the disc is simple

harmonic.

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 of the support .The period of oscillations is given by

T=2π√I/c ------------(1)

Where I is the moment of inertia of disc about the axis of rotation &’c’is the couple per unit twist of

the wire.

But

c = (πηa4 ) ----------------(2)

2l

Where a is the radius of the wire,

l is its length and

η is the rigidity modulus

from eq’s 1&2 we have,

η=8πI ( l/T2) -----------------(3)

a4

In case of a circular disc(or cylinder) whose geometric axis coincides with the axis of

rotation,the moment of inertia I is given by

I = MR2 ------------------ (4)

2

Where M is the mass of the disc

R is the radius

On substituting eq (4) in (3)

η = 4𝜋𝑀𝑅2

𝑎4 (𝑙

𝑇2) dynes/cm2

M is Mass of the disc

R is Radius of the disc

a is Radius of the wire

l is Length of the wire between the two chuck nuts

T is Time period

Table: - 2

Radius of the wire (a)

Screw gauge error = correction (n) = L.C. =

S.No. PSR

(x) (mm)

HSR

Corrected

HSR(n1)=HSR±n

y= (n1 x LC ) Diameter (d) = x + y

(mm) Radius (a)=

𝒅

𝟐

(mm)

1.

2.

3.

4.

GRAPH:-

A graph is drawing between “l “on X-axis and T2 on Y-axis.

T2

(se

l (cm)

PROCEDURE

Torsional pendulum consists of a uniform circular metal (brass or iron) disc of diameter about 10cm and

thickness of 1 cm. Suspended by a metal wire (whose η is to be determined) at the center of the

disc.The other end of the wire is griped into another chuck, which is fixed to a wall bracket. The

length (l) of 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 into oscillations in the horizontal plane, by

turning 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 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 screw gauge , 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.

OBSERVATION S:

Mass of the disc (M) = ------------ gm

Radius of the disc (R) = ------------- cm

Radius of the wire (a) = ------------- cm

Average of l/T2 (from table) = -----------cm/sec2

Value of l/T2 (from graph) = ------------- cm/sec2

(1N/m2 = 10 dynes /cm2 )

( 1 N = 105 dynes)

PRECAUTIONS:

1. The wire should be free from kinks. 2. The disc should not wobble. 3. The reading should be made correctly.

RESULT:

The Rigidity modulus (η) of given wire is (from table) dyne/cm2

The Rigidity modulus (η) of given wire is (from graph) dyne/cm2

Conclusion : The given wire is made up of---------------- material.

DIAGRAM: - Interference in thin air film

Eye piece

Plano convex lens

Plain glass

plate

NEWTON’S RINGS EXPERIMENT

AIM: - To find the radius of curvature of the surface of the lens, by forming Newton’s rings.

APPARATUS: - Traveling micro scope, Sodium vapour lamp, Plano convex lens, 450 angle glass plate set

up, Reading lens, Reading lamp.

THEORY: -

Newton’s rings are formed because of the interference between the waves reflected from top and bottom surfaces of the air film formed between the plain glass plate and plano-convex lens. When light incident on combination of glass plate and plano-convex lens system one part of the ray will be reflected back from glass-air interface without any phase difference and the same ray is reflected from glass plate with phase difference of π. Because of interference between these two rays with phase and without phase there will be formation of circular rings.

The radius of curvature of the curved face of the lens is:

Where Dm=Diameter of the mth ring.

Dn=Diameter of the n th ring.

λ = Wave length of Sodium vapor lamp.(5893A0)

m= mth fringe

n = nth fringe

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,

R = 𝑫𝒎

𝟐 −𝑫𝒏𝟐

𝟒𝛌 ( 𝐦−𝐧) cm or A

0------------ (1)

if necessary, turning 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

ring is noted. The microscope is moved in the right direction from the center and corresponding to the 2nd,

4th, 6th-------20th dark ring on the right side are noted. Readings are to be noted 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 curvatureis determined by a spherometer.

OBSERVATIONS:

1. Wave length of Sodium vapour lamp (λ)

2. Least count of travelling microscope = 1 MSD/VS =

TABLE: To determine the square of the diameter of the different fringes

No. of

Ring

Microscope Reading Left side

(L)

Microscope Reading Right side

(R)

Diameter(D)

T.R L ~ T.R

(cm )

D2

(Cm2) MSR

(a)

(Cm)

VC

(b)

T.R L=a+(b x LC)

(Cm)

MSR

(a)

(Cm)

VC

(b)

T.R R=a+(b xLC)

(Cm)

20

18

16

14

12

10

8

6

4

2

GRAPH:

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 a straight line as shown in the fig.

From graph the values of Dı² and D2 ² 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 from standard tables.

Y

Dm²

D² (cm2)

D n ²

n m X

no. of fringes

PRECAUTIONS:

1. Wipe the lens and glass plates with cloth before starting the experiment.

2. The center of the ring must be dark.

3. Use reading lens with light while observing the readings. 4. Before starting the experiment make sure that the movement of microscope in both sides (left and

right side) of the rings.

RESULT:

The radius of curvature of Plano - convex lens is = cm/A0

Ray Diagram :

Table : To determine total number of lines on plain transmission grating .

Distance

between

grating

and

screen

(D)

(cm)

Order

Left side

d1

(cm)

Right side

d2

(cm)

Mean

d= (d1+d2)/2

(cm)

𝒔𝒊𝒏𝜽

=𝒅

√𝒅𝟐 + 𝑫𝟐

(cm)

N = 𝐝𝐬𝐢𝐧Ө

𝒏𝝀

1

2

3

4

Avg =

Experiment-11

WAVE LENGTH OF LASER RADIATION-Grating

AIM: To determine the number of lines present on given plane transmission grating using laser

source .

APPARATUS: Diffraction grating, laser beam of Semiconductor source, meter scale and prism

table.

FORMULA: n.Nλ = dsinӨ A0

N = number of lines on the student grating per inch ?

d= distance between orders

D = distance between screen and grating

Ө = angle of diffraction

THEORY:

An arrangement consisting of large number of parallel slits of the same width (e) separated

by equal opaque space (d) is known as the “diffraction grating”. (e+d) is known as the grating

element.

Hence (e+d) = l” (1 Inch) = 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 is number of lines per inch on the plane diffraction grating and n is order of diffraction

light.

N = 𝐝𝐬𝐢𝐧Ө

𝒏𝝀

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 orders with decrease in

intensity are seen on the screen. The light next to central maxima is first order 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” on left side and the distance between central maxima to first order on the right side is “d2” and

take the average of the “d1” “d2” .The same procedure is followed for the second order.

Substitute the values for Sin θ and determine the values of wavelength of laser

radiation.

PRECAUTIONS:

1) Do not look at the laser beam directly.

2) The prism table should be perpendicular to the laser.

3) Laser beam and the grating should be horizontal.

RESULT:

The total number of lines present on given plane transmission grating = ----------

Prism table

Direct reading

Telescope(T1 & T2)

EXPERIMENT: DISPERSION OF LIGHT (Spectrometer – Prism)

AIM: - To determine the dispersive power of the material of the given prism by the spectrometer.

APPARATUS: - Spectrometer, Source (Mercury Vapour Lamp), Prism, Magnifying

lens with light , Spirit level

THEORY: -The essential parts of the spectrometer are: (a) The telescope, (b) The

collimator & (c) Prism table.

(a) The Telescope: -

The telescope is an important part in Telescope. At one end of a brass tube is an

objective, at the other end a (Rams den’s) eyepiece and in between, a cross wire

screen. The eyepiece 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 points. 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.

OBSERVATIONS: -

Least count of the vernier of the spectrometer LC =

Angle of prism A =

Direct reading Vernier (LHS) V1= MSR + (VCXLC) =

Vernier (RHS) V2= MSR + (VCXLC) =

Table : Angle of prism (A)

S No Telescope reading left side Telescope reading right side 2A=

T.RL ͠T.RR

A= 𝐓.𝐑𝐋 ͠𝐓.𝐑𝐑

𝟐

M.S.R

(a) Degree

V.C

(b)

T.RL= a+(b x LC) M.S.R

(a) Degree

V.C

(b)

T.RR= a+(b x LC)

Table : Direct Reading

Telescope reading

MSR (a) V.C (b) T.R = a+ ( b x LC )

TABLE :- Angle of minimum deviation ( δm / Dm)

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

colors Reading of the deviated ray Angle of deviated

ray

Mean

(D)

𝑋 + 𝑌

2

µ = sin(

𝐴+𝐷

2)

sin(𝐴

2)

LHS (VL) RHS(VR)

V1~ VL

(X)

V2~ VR

(Y)

MSR

(a)

VC

(b)

T.R =a+(b x LC)

(VL)

MSR

(a)

VC

(b)

T.R =a+(b x LC)

(VR)

Blue

Red

Green

Violet

meters way and the eyepiece is adjusted so that the 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 object 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 the other. The prism is kept in one

of these positions and (say) the telescope is adjusted until the image is clear. 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 the 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.

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.

FORMULA :-

The refractive index of the material of the prism is given by

2sin

2sin

A

DmA

Where A is the angle of the equilateral prism and

Dm is the angle of minimum deviation.

The dispersive power (ω) of the material of the prism is given by

1

RB

Where µB= the refractive index of the blue rays

µR = the refractive index of the red ray and

2

RB ; the mean of µB and µR

PROCEDURE: -

1. 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. The vernier table is then fixed

with the help of vernier screw. 2. The ray of light passing through the collimator strikes the polished surface BC

of the prism and undergoes deviation.And emerges out of the prism from the face AC.

3. The deviated ray (continuous spectrum) is seen through the telescope in

position T1. Looking at the spectrum the prism table is now slowly moved on

to one side, so that the spectrum moves towards undeviated path of the

beam.

4 . The deviated ray (spectrum) also moves on to the same side for some time

and then the ray starts turning back even through the prism table is moved in

the same direction. The point at which the ray starts turning back is called

MINIMUM DEVIATION POSITION.

5 . In the spectrum, it is sufficient if one colour is adjusted for minimum

deviation position. In this limiting position of the spectrum, deviation of

the beam is minimum.

6. 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 1 and vernier 2

and tabulated. The reading is called the minimum deviation reading for the

blue colour.

7. The telescope is now moved on the red colour and the readings are taken as

explained for blue colour.

8. 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 1 and vernier 2 are noted.

9. The difference of readings between the deviated reading for blue colour and

the direct reading gives the angle of the minimum deviation for the blue colour.

10. 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.

11. The refractive indices for the blue and red rays are calculated using

equation and the dispersive power of the material of the prism is

calculated.(the angle of the equilateral prism, A = 60°).

PRECAUTIONS:

1. Don’t touch polished surface of the prism with hands to avoid finger prints. 2. Use reading lens with light while taking the readings in vernier scale. 3. The mercury light should be placed in side a wooden box.

RESULT:

Dispersive power of the material of the prism (ω) = ------------

Dispersive power of crown material = -------

Hence the given material of prism is ------------------

CIRCUIT DIAGRAM

GRAPH:

OBSERVATIONS:

Self inductance of the coil, L =

Capacity of the condenser, C =

Resistance of the resistor, R =

Input voltage of the A.C, Vi= volt

S.No. Frequency f(KHz) Current, I(mA)

LCR - Series Resonance

AIM:

To study the frequency response characteristics of L.C.R. Series resonance circuit and to determine

the resonance frequency and quality factor.

APPARATUS:

A signal generator, vacuum tube voltmeter, a milli ammeter, condenser, an inductance coil, a

resistance box and connecting wires.

FORMULA:

Theoretical Formula:

1. Resonance frequency of the series resonant circuit is,

fo = LC2

1

2. Quality factor of the circuit is,

Q = C

L

R

1

Where R = resistance of the resistor (ohm)

L = inductance of the coil (henry)

C = capacitance of the condenser (farad)

Experimental Formula:

1. Resonance frequency of the circuit, fo = Hz

(From the graph)

2. Bandwidth of the resonant circuit, ∆f = (f2- f1)

(From the graph)

Where f1 = lower half power frequency

f2 = upper half power frequency

3. Quality factor of the circuit, Q = f

fo

THEORY:

A coil of self inductance L, resistance R and condenser of capacitance C are connected in series

with a source of A.C.Supply as shown in the circuit. This circuit is known as L.C.R.circuit. Where an

alternating voltage of a pure sine waveform which is represented by,

E = Eo sin t

Is applied to the circuit, then an A.C. will flow through the circuit. The current flowing through the circuit at

any instant is given by,

I = Io sin t

Where E = instantaneous value of the applied voltage

Eo = maximum or peak value of the alternating voltage.

I = instantaneous value of the current

Io = maximum or peak value of the current

= angular frequency of the A.C supply

= 2 f

f = frequency of the alternating voltage

t = phase angle

= 2 f t

Due to the applied E.M.F i) an E.M.F ( L dt

di) is induced in the inductance which oppose the applied

E.M.F ii0 there is a potential drop (Ri) across the resistance and iii) a potential difference (Q?C) is developed

across the plates of the condenser, then, according to Ohm’s law,

Eo Sin RIC

Q

dt

dILt

tSinERIC

Q

dt

dIL o

Where Q = charge on the plates of the condenser at an instant

I = instantaneous value of the current in the circuit

The peak value of the current is given by

2

2 1

CLR

EI o

= 22 )( CL

o

XXR

E

Where, XL = fLL 2 inductive reactance of the circuit

XC =fcc 2

11 = capacitive reactance of the circuit

The total resistance offered to flow of current in the A.C.circuit is called the impedance (z) of the circuit or

effective resistance of the circuit.

The impedance of the circuit z=

2

2 1

CLR

Io = Z

Eo

The phase difference between the current in the circuit and the E.M.F applied to the circuit is given by,

R

CL

Tan

1

From above equation, it is obvious that whether the current in the A.C.circuit leads the E.M.F or lags behind

the E.M.F. depends on the magnitude of the inductive reactance, L as well as on the capacitive reactance

C.

Special case:When, C

L

1

, then Tanθ = 0, Z=R and I=R

Eo

In this case, the current and the applied E.M.F are in phase with each other. This condition is known as

resonance. So, the current in the circuit depends only on the value of R. If the value of R is small, the

impedance of the circuit is minium. Consequently, maximum A.C will flow through the circuit and the circuit

is said to be in tune or resonance with the applied voltage. The frequency at which L =C

1

Is called the resonance frequency, fo and the circuit is known as the series resonance circuit.

L =C

1

orLC

12

LC

o

1 , = o at resonance

LC

fo

12

LCfo

2

1

PROCEDURE:

A coil of self inductance L , a condenser of capacity C , a resistance R(10 ) and a milliammeter a

are to be connected in series with the signal generator as shown in the circuit. Switch on the signal

generator. Adjust the frequency nob of the signal generator so that the frequency, f of the A.C.signal is 2

KHz. Adjust the amplitude of the input signal to a convenient value by means of V.T.V.M. i.e., the input

voltage Vi. Then, note the current I, in the circuit shown by the milliammeter A.

Increase the frequency, f of the input signal in convenient steps (say 1 KHz), keeping input voltage,

Vi constant throughout the experiment. Then the current increases slowly at the beginning, afterwards

increases sharply and then reaches a peak value called the sharpness of the resonance. This will happen

when the frequency of the applied voltage is equal to the natural frequency of the circuit i.e., resonance

occurs. This frequency at which the current reaches a peak value is called the resonance frequency, fo. At

the resonance frequency, the current is maximum and the impedance is minimum. Again increase the

frequency of the input signal beyond the resonance frequency, and then the current through the circuit

gradually decreases. Note the observations in table.

Repeat the experiment b introducing different values of R in the circuit, for the same values of L

and C, keeping the input voltage Vi constant throughout the experiment. The theoretical values of the

resonance frequency, fo and the quality factor, Q can be calculated using the formulae.

GRAPH:

Draw a graph with the frequency, f on the x-axis and the current I on the y-axis. A sharp resonance

curve will be obtained. From the graph, note the maximum current, Io and thecorresponding frequency at

which the current is maximum. This frequency is called as the resonance frequency f0.

To determine the bandwidth (∆f ) and quality factor Q:

From the graph, find the value of Io/ 2 . Mark the value on the y-axis. From the value draw a line

parallel to x-axis. This line cuts the curve at two points A,B< called half power points. From the points A and

B, draw lines parallel to y-axis, which meets the x-axis at two points corresponding to two frequencies f1

and f2 called the half power frequencies, on either side of the resonance frequency fo.

Bandwidth of the circuit, ∆f = (f2- f1) KHz

Quality factor of the circuit, Q = f

fo

Also draw a graph with frequency f, along the x-axis and the impedence Z along the y-axis.The theoretical

and experimental values of the resonance frequency fo and the quality factor Q are to be compared.

CALCULATIONS:

1. Theoretical values:

i) L = ----------henry C = --------farad R = -----------

Resonance frequency, fo = LC2

1 = --------------Hz

iii) Quality factors, Q = C

L

R

1= ---------

Experimental values (From graphs)

i)Resonance frequency,f0 = ------KHz = ------Hz

ii) Band width, f = (f2 – f1) = ------KHz = -------Hz

iii)Quality actor Q = f

f

0 = -----

PRECAUTIONS:

1. A fixed amplitude of voltage should be applied to the circuit for the selected values of L,C and R at different frequencies.

2. The input voltage applied to the circuit should be checked at all the frequencies.

RESULT:

The theoretical and experimental values of resonance frequency, fo and the quality factor Q, are

calculated and compares. They are found to be equal.

S.No. Type of connection Parameter Theoretical Experimental

L1C1R1 L1C1R1

1 Series Resonance

Resonance frequency

foHz

2 Quality factor Q

Lab 2: coupled oscillators

1 Introduction

In this experiment you are going to observe the normal modes of oscillation of several different me-

chanical systems, first on the air tracks and then using some coupled pendula. The normal modes of

motion of a system of coupled oscillators are ‘stable’ with respect to time. That is, if you start the

masses of a system oscillating in one of the normal modes and observe it for some time, the motion will

have constant characteristics as its amplitude decays because of the ever present friction forces. Also,

the frequency of oscillation of all the masses in the system is the same, and each of the masses

executes simple harmonic motion at this frequency. The frequency is called the natural frequency of the

normal mode or an eigenfrequency of the system. There are certain relationships between the

eigenfrequencies and the frequencies of the uncoupled oscillators that will be discussed later. If a system is excited into oscillations that are a mixture of normal modes, then the motion will

change character over a period of time. Perhaps one of the masses will decrease amplitude and pass

its energy to another mass, which will later pass the energy back. Such motion is clearly different from

simple harmonic motion and therefore does not constitute a normal mode, even though the oscillations

are all at the same frequency. The exchange of energy generally occurs at a frequency that is quite

different from the oscillation frequency. (Read this paragraph a second time.)

2 Theory

Begin your study with two equal mass gliders on the air track as shown in Fig. 1. If the masses are

not equal, certain complications arise that can obscure the simplicity of the motion, so you should

remove all extra weights, clips, etc. and be sure that you have two sails of equal mass that you can

mount on these gliders for damping the motion by air friction. The two gliders are coupled together

with a spring as shown in the diagram. This coupling is somewhat tighter than the coupling you will

later use with the two pendula, but it is not perfectly rigid; with a rigid bar the system would have

only one mode of oscillation because the gliders would not be able to move relative to one another.

M M

to

X

motor

X1 X 2 3

Figure 1: The two masses and

three spring constant are

equal. At equilibrium, the three

lengths xi are also equal. The

motor can only drive one end

of one spring, but at reso-

nance the energy is distributed

among the masses.

If you displace the gliders symmetrically from their initial equilibrium positions and release them,

their oscillations will die down in time, but the relative displacements of the two gliders will maintain a

constant relationship. For example, if you push them toward one another by the same amount and

release them, the displacement of one will always be equal in magnitude but opposite in direction

the displacement of the other. If you displace them both to one side by an equal amount

and release them, they will oscillate together in a way that preserves their equilibrium

separation. You should be able to observe both of these normal modes of oscillation with

the pair of coupled masses before you go any further. You should observe that the two normal modes described above have different

frequencies. Mea-sure these frequencies. You should rotate the sails on the gliders so that they are parallel to the air track to minimize damping in order to do this part of the experiment. There will then be many oscil-lations for you to count before all the energy of the system is lost. Now hold one of the masses fixed and measure the oscillation frequency of the other mass. Also, fix the second mass and measure the oscillation frequency of the first one. What is

the relationship among the four frequencies you have measured? q In the case of one mass vibrating with the other held fixed the frequency is simply ! = 2k=M

since the restoring force on the displaced mass is 2kx (because there are two springs each con- tributing kx). For the oscillations with the distance between the gliders constant, the frequency is q ! = 2k=2M since there might just as well be a massless rigid bar between the gliders making it a mass of 2M oscillating under the same conditions as the single mass above. For the case of the q masses oscillating in opposite directions, the frequency is ! = 3k=M since the restoring force from the middle spring is 2kx (its stretch is twice the displacement of either mass) plus the normal restor-ing force from the outside spring. The frequencies you measure

should therefore be in the ratio of 1 : p

2 : p

3. Also notice that the sum of the squares of

the individual oscillation frequencies (first one mass fixed and then the other) is equal to the sum of the squares of the frequencies of the normal modes. This is not an accident!

It is constructive to consider the motion of the center of mass (CM) of the system of

gliders in each of the normal modes. In this case it is easy: in the high frequency mode

(called the optical mode) the CM remains fixed at the middle of the center spring. You can

hold the spring at this point without disturbing the oscillation. This point is called a node of

the motion. In the low frequency normal mode (called acoustical mode) the CM oscillates

at the acoustical frequency. In the optical mode there is motion with respect to the CM, but

the CM is stationary. In the acoustical mode there is no motion with respect to the CM, but

the CM moves. These are general properties of these two types of modes. Consider the motion of the gliders with respect to the CM. How does the motion look from a

coordinate system moving with the CM in each of the normal modes of oscillation? Describe it.

3 Procedure

The normal modes of motion represent the way a system of coupled masses oscillates naturally. In

order to see what happens to a system of coupled oscillators driven at some frequency, consider the

analogy to the case of a single mass where the motion is oscillatory at the driving frequency with an

amplitude that is a maximum when the driving frequency is equal to the natural frequency. Since the

coupled oscillators have two natural frequencies you might expect there to be two resonant maxima in

the amplitude of the driven motion. In order to test this, you should mount the sails on the gliders for

damping and proceed to drive them at various frequencies using the variable speed motor. You should

record the amplitude of oscillation of each mass as a function of the driving frequency and plot the

result. You should observe two resonant maxima for each mass as shown in Fig. 2, and the maxima

2

should occur near the natural frequencies you have already measured. Figure 2: The two reso-

nances at the eigenfrequen-

cies can be mapped out as

shown. They are at differ-

ent frequencies, and may

have different heights

and/or differ-ent widths.

1.0

Amplitude 0.8

0.6

0.4

0.2

0.0

ω

Optional Advanced Work: If you would like to do some advanced work on this system you should go

through exactly the same procedure for three coupled masses. There are now three normal modes.

You might guess that one of them is an acoustical mode similar to that of two masses in which all three

masses move together as if they were connected with rigid rods. This is a good guess but it’s not

correct simply because this middle mass would be expected to oscillate but the sum of the forces on it

from the two springs would always be zero. This is because these springs retain their equilibrium

length. It is therefore necessary that the middle mass oscillate with a larger amplitude but at

approximately the same phase as the outside masses in the acoustical mode. This mode is hard to observe by starting the gliders oscillating at some point because you don’t know the amplitude of the q center glider. The frequency would be ! = 2k=3M as long as all three gliders have equal mass.

A little thought might lead you to guess that another normal mode consists of the two end masses

oscillating in opposite directions with the center one perfectly stationary. You can verify this by starting

the motion and then seeing if it maintains itself and if both the masses oscillate with the same

frequency. Actually the center one can be said to oscillate at that frequency too, but with zero

amplitude. If you do it carefully, the middle mass will never move as the oscillation of the end ones

out. Show that the frequency of this oscillation is given by ! = 2k=M. dies

The third normal mode is a little more difficult to discover by q

simply studying the equipment. You can find it by putting the sails on the gliders and driving the system at various frequencies. You can

find the approximate frequency by using the rule of the sum of the squares of the frequencies described before. The oscillation frequency of each individual mass, if the the others were clamped, q is ! = 2k=M (they’re all equal) and so the sum of the squares is 6k=M. The two frequencies we have discussed can be squared and summed to give (8=3)k=M so the frequency of the third normal q mode is expected to be ! = 10k=3M. This is higher than the other two frequencies, but if is

still within the range of your motors. You should measure the oscillation frequencies of the

clamped masses to verify the above calculation, and when you find the normal mode, you

should verify the sum of the squares relation. Plot the amplitude of oscillation of one of the masses versus frequency and you will find three

resonance maxima, two of which correspond to the normal modes we have already predicted. Observe

the first normal mode and measure the amplitude and phase of the center glider. Observe the third

normal mode and measure its frequency. If you set the drive at the resonance frequency of any of the

modes and then switch off the motor, will the oscillations decay without changing frequency and still

maintain the characteristics of the motion? If you are careful, you should be able to observe this. 3

Consider the motion of the CM of the three coupled oscillators. Describe the motion of

the CM for each of the three normal modes of oscillation. Describe the motion of each of

the gliders with respect to the CM for each of the three normal modes. Could you do this

for motion of the system which is a mixture of normal modes?

4 Hints and Kinks Department

You must remember to wait some time for oscillations at the undesirable frequencies to die out

after you change the driving frequency of the variable speed motor. Otherwise you will have the

kind of problems of mixed modes described at the end of Experiment 1, namely, the motion will be

a super-position of two or more frequencies. With coupled oscillators the system is much more

complicated and too difficult to analyze in that simple way, so it’s important to be patient. The damping time of an air track glider with sail is also considerably longer than the

spring in Experiment 1. You may want to measure it by clamping one glider and just

watching the other one’s oscillations damp out (of course, with no drive). Suffice it to say

that the motion at any frequency which is not a pure eigenfrequency will decay into a

superposition of the normal modes of the system resulting in a rather complicated motion. It is very important to match the masses of the system as closely as possible. If you don’t,

the normal modes will not be symmetrical in the coordinate displacements. Of course normal

modes exist for any system, whether or not the masses are equal. Usually the displacements

are inversely proportional to the masses so that the CM of the system behaves in the same

way as the center-of-mass of a system with equal masses. Remember that the sails do not

have zero mass, so that the measurements you make of the resonant frequencies with other

masses clamped should have the sails mounted but turned parallel to the track. Be sure you do not drive the system into oscillations that are so large that the springs

pop off. Be careful not to overheat the motors.

5 Coupled Oscillators With Variable Coupling

Connect the strings of two pendula with a massless (almost) rigid rod such as a soda straw.

You can do it by cutting short slits in the ends of the straw and slipping the string of each

pendulum into the slits at the end of the straw. The distance between the pendulum strings

should be just a few mm less than the length of the straw. You should slide the coupling rod up

the string until 9/10 or more of the string is below the coupling. Find and describe the normal

modes of oscillation in the plane of the strings of this system of coupled oscillators (hint: there

is an acoustical and an optical mode). What are the frequencies? Show that the measured

values of the frequencies are consistent with the expected values. Do they also satisfy the sum

of the squares rule? (How would you ‘clamp’ one of the masses in this case?) You should observe and measure the frequencies of the normal modes for several different heights

of this coupling bar. Make a plot of the frequencies of the normal modes versus height of the coupling

bar. Is the result what you expect? Why or why not? Prove that the frequency of one of the normal

modes is independent of the height of the bar, and that the other normal frequency depends on the

4

PHY 300 Lab 2 Fall 2009

square root of the distance from the bar to the pendulum bob. Which is the optical mode

and which is the acoustical? Put the bar near the top of the strings, displace one of the pendulum bobs, and release it. What

happens? Describe the motion in detail. Go back and read the second paragraph of this write-up for a

third time. How long does the phenomenon you observe take? This time depends on the degree of

coupling and therefore on the height of the bar. Measure the time it takes versus height of the bar and

make a graph. Does the curve look familiar? Is it related to anything we have done before? Is it related

to the eigenfrequencies? How? Plot the time for energy transfer versus eigenfrequency to find out.

Speculate on the formula for the time versus bar height graph. Can you derive it? If you put the bar too low (lower than about 1/2 of the length of the strings) you will find that

there is substantial coupling to another normal mode of oscillation, the torsional mode. Be careful

to avoid it in the measurements above, but if you choose to do advanced work on this experiment

you should study this mode as well as other normal modes of oscillation of the system. There are a

total of four normal modes - why is this? Can you observe them all? Describe them. For further advanced study you should try coupling three pendula by putting a slit in the

middle of the straw and slipping the string of a third pendulum into it (see Fig. 3). What

measurements can you make with this system? What can you predict about the results?

Can you describe the motion of and with respect to the CM? Can you do it for just two

pendula? Can you verify your predictions about the motion?

Figure 3: The left side shows

three coupled pendula, al-

though you’ll start this exper-

iment using only two

pendula. On the right is a

“compound pendulum”,

which is simply another form

of coupled oscil-lators.

You should also make a double pendulum, as shown on the right side of Fig. 3. What

are the normal modes of motion? What are their frequencies? Make measurements. Do

the frequencies obey the sum of the squares rule? There are many options open to you in this experiment. Pick one or some of them that

interest you and do them. Work carefully and accurately so that your efforts will not be wasted.

It is better to do a small amount of work well than to try everything and do a sloppy job.

6 Hints and Kinks Department

Pick an amplitude that is large enough to be easily observable, but not so large that the

pendulum weights collide. Remember also that a pendulum only executes simple

harmonic motion if the maxi-mum of excursion is a few degrees. In both this and the air track experiments you should try to keep the oscillating masses

from being disturbed by random air currents. Don’t move around excessively, and don’t

breathe on the oscillators while you are trying to take measurements.

©

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1

EXPERIMENT: 1 LOSSES IN OPTICAL FIBER AT 660nm AND 850nm

1.1 Aim of the Experiment:

The aim of the experiment is to study various types of losses that occur in optical fibers and measure losses in dBm of two optical fiber patch cords at two wavelengths. Viz. 660 nm and 850 nm.

Theory: Attenuation in an optical fiber is a result of following effects:

Losses at connectors and losses due to the length of the fiber cable. The optical power at a distance L, in an optical fiber is given by PL α PoL, Where Po is the input power and α is the attenuation coefficient in decibels per length. The typical attenuation coefficient value for the fiber under consideration is 0.2dBm per meter at a wavelength 660nm.

Losses in fiber occur at fiber-fiber joints or splices due to axial displacement, Angular

displacement, separation (air core), mismatch of course diameter, mismatch of numerical aperture, improper cleaving and cleaning at the ends. The loss equation for simple fiber optic link is given by:

Pin(dBm)-Pout(dBm) = Lj1+LFIB1+Lj2+LFIB2+Lj3(dB): Where Lj1(dB) is the loss at LED

connector junction, LFIB1(dB) is the loss in cable1, Lj2(dB) is the insertion loss in a line

connector, LFIB2(dB) is the loss in cable2, and Lj3(dB) is loss at the connector detector

junction.

NOTE: In this particular experiment connections to Voltmeter (M1), Signal generator are not required. Connect the circuit as mentioned below in the experiment procedure.

Experiment Procedure for IR L.E.D 850 nm ( Infra Red Light Emitting Diode ) :

We are mainly finding losses in optical fibers due to its length and bending.

Following procedure is for study of losses due to length of optical fibre using 850nm L.E.D. 1. Short M2 of I.R L.E.D ( +ve and –ve terminals ) on the Tx unit with patch cords ( for this experiment M2 is not required ) .

2. Relieve all the twists and strains in the fiber cable, ensure that it is as straight as possible, as shown in fig.1.1.

3. Connect one end of the cable 1 ( 1 meter ) to the 850nm LED FC ( Fiber Connector ) adapter of the Tx unit and other end to the PIN diode FC ( Fiber Connector ) adapter of Rx unit as shown in figure 1.1.

4. Move the S1 switch on Rx unit towards 850 nm IR LED.

5. Switch ON the AC mains of both Rx & Tx units.. 6. Rotate Po ( Power Adjustment potentiometer ) pot to extreme clockwise direction to set

maximum carrier power, note down the “Optical Power Meter Reading “ P1 in µW on Rx unit. 7. Without altering the position of Po ( Power Adjustment potentiometer ) pot, Connect cable 2 (

3meters ) between 850nm FC adapter and PIN diode FC adapter of Rx Unit. Note/Tabulate “Optical Power Meter Reading “, P2 on th Rx unit.

2

8. Without altering the position of Po ( Power Adjustment potentiometer ) pot, Connect cable 3 (

5 meters ) between 850nm FC adapter and PIN diode FC adapter of Tx Unit. Note/Tabulate “Optical Power Meter Reading “, on the Rx unit, P3 ( As per table 1.1 ).

9. Convert the all power meter readings in µW to dBm using formula. Given below. dBm=10*log (Power meter reading in mW/1mW)

In this case, dBm=10*log (Power meter reading in µW/1000) 10. Tabulate all the readings in table 1.1 11. Calculate average loss per meter at 850 nm. The loss per meter in the range of 2±0.5 dBm is acceptable ( As per standards ) .

Experiment Procedure for L.E.D 660 nm ( Light Emitting Diode ) :

Following procedure is for study of losses due to length of optical fibre using 660nm L.E.D.: 1. Short M2 of 850nm LED ( +ve and –ve terminals ) on the Tx unit with patch cords ( for this

experiment M2 is not required ) . 2. Relieve all the twists and strains in the fiber cable, ensure that it is as straight as possible, as

shown in fig.1.1. 3. Connect one end of the cable 1 ( 1 meter ) to the 660nm LED FC ( Fiber Connector ) adapter

of the Tx unit and other end to the PIN diode FC ( Fiber Connector ) adapter of Rx unit as shown in figure 1.1.

4. Move the S1 switch on Rx unit towards 660 nm L.E.D.

5. Switch ON the AC mains of both Rx & Tx units. 6. Rotate Po ( Power Adjustment potentiometer ) pot to extreme clockwise direction to set

maximum carrier power, note down the “Optical Power Meter Reading “ P1 in µW on Rx unit.

7. Without altering the position of Po ( Power Adjustment potentiometer ) pot, Connect cable 2

( 3meters ) between 660nm FC adapter and PIN diode FC adapter of Rx Unit. Note/Tabulate

“Optical Power Meter Reading “, P2 on th Rx unit.

8. Without altering the position of Po ( Power Adjustment potentiometer ) pot, Connect cable 3

( 5 meters ) between 660nm FC adapter and PIN diode FC adapter of Tx Unit. Note/Tabulate

“Optical Power Meter Reading “, on the Rx unit, P3 ( As per table 1.1 ).

9. Convert the all power meter readings in µW to dBm using formula. Given below. dBm=10*log (Power meter reading in mW/1mW)

In this case, dBm=10*log (Power meter reading in µW/1000) 10. Tabulate all the readings in table 1.1 11. Calculate average loss per meter at 660 nm. The loss per meter in the range of 0.2 dBm is

acceptable ( As per standards ) .

Experimental Procedure for losses due to OF Bending using 850nm L.E.D:

STEP 1: Short the M2 +ve and –ve terminals of both LED’s on Tx unit, and Connect one end of the cable 1mtr to the 850nm LED FC adaptar of the Tx unit and other end to the pin diode FC adaptor of Rx unit as shown in figure 1.1. Move the S2 switches on Tx unit towards 850 nm IR LED input. Then turn on the AC mains. STEP 2: Relieve all the twists and strains in the fiber cable so that it is straight as shown in fig.1.1 STEP 3: Rotate P0 pot to the extreme clockwise direction to get maximum intensity and note down the reading(P01) of power meter on Rx unit..

3

STEP 4: Now wing one turnt of he OF cable on mandrel and note down the new reading P02. STEP 5:Repeat the experiment for 3meter and 5 meter cables with more turns and tabulate the readings in the tabular column 1.3 STEP 6:Above experiment can be repeated for 660nm LED also. Note: 1. Do not repeat the bending losses experiment more than 3 turns as it may cause

permanent damage to FO cable.

2. While doing experiment with 660nm LED move switch towards 660nm input.

3. Convert the all power meter readings in µW to dBm using formula. Given below. dBm=10*log (Power meter reading in mW/1mW)

In this case, dBm=10*log (Power meter reading in µW/1000)

TX Unit Rx Unit

A

660nm PT FC

S1

M2 850nm Pin FC PM

OF cable

Fig 1.1

1 meter cable

3 meter cable

5 meter cable

4

Table 1.1

Table of readings for 850nm

SI P1 Rd1 P2 Rd2 P3 Rd3 M0=Rd1-Rd2/2 M1=Rd2-Rd3/2 M2=R1-R3/4 L/M

No. in µW(dBm)in µW(dBm) in µW (dBm) (dBm) (dBm) (dBm) (dBm)

Table of readings for 660nm

SI P1 R1 P2 R2 P3 R3 M0=R1-R2/2 M1=R2-R3/2 M2=R1-R3/4 L/M

No. in µW(dBm)in µW(dBm) in µW (dBm) (dBm) (dBm) (dBm) (dBm)

Where L= Mo + M1 + M2

3

Table 1.3 Table of readings for 850nm n=No of Turns on mandrel……… Cable P01 R01 P02 R02 R01-R02 P11 R11P12 R12 R11-R12

No of

L in µW in dBm in µW in dBm

n

in µW in dBm in µW in dBm

Turns(n)

n

1 mtr

3 mtr

5mtr

5

EXPERIMENT 2: CHARACTERISATION OF 660 NM AND 850 NM L.E.D.

Aim of the experiment 2.1: The aim of the experiment is to study the relationship between the LED dc forward current and the L.E.D. optical power output and determine the linearity of the device at 660nm as well as 850 nm. Theory: L.E.D and Laser diodes are commonly used sources in optical communication systems, whether the system transmits digital or analogue signals. In case of analogue transmission, direct intensity modulation of optical source is possible, provided the optical out put from the source can be linearly varied as a function of the modulating electrical signal amplitude. L.E.D have a linear optical out put with relation to the forward current over a certain region of operation. It may be mentioned that in many low cost, short-lenght and small bandwidth applications, L.E.D at 660nm, 850nm and 1300nm are popular. While direct intensity modulation is easy to realize, higher performance is achieved by FM modulating the base band signal prior to intensity modulation. The relationship between an L.E.D optical output Po and the L.E.D forward current Iғ is given by Pо=K *Iғ (over a limited range) where K is constant.

Experiment Procedure:

1. Connect one end of the cable1(1mtr) to the 850nm L.E.D. FC adaptor of Tx unit and the

other end to the PIN photodiode FC adaptor of Rx unit. 2. Connect on board Ammeter to 850nm IR L.E.D M2 meter (to its respective +ve and –

ve terminals) provided on the circuit panel of the Tx unit as shown in fig 2.1, Move the S2 switch on Rx unit towards 850 nm IR LED and Then turn on the AC mains.

3. Rotate Po pot to the extreme anticlockwise direction to reduce the Iғ (L.E.D. forward current) to 0Amps and power meter should be zero.

4. Slowly rotate the Po knob in clockwise direction to increase Iғ. The power meter should read 5µW approximately. 5. Now change Iғ in steps of 3mA by rotating Po in clockwise direction and note the

power meter readings. 6. Tabulate the readings as in Table 1.2. and Repeat the above complete experiment for 660nm L.E.D. also.

AC AC

Tx Unit Rx Unit

A660nm PT

P0 OF Cable

850nm Pin PM

6

M2

Fig 2.1

Table for 850nm LED

Table 1.2

SI IF in mA Power mtr reading Power mtr reading

In µW in(dBm)

1.

2.

3.

4.

Table 1.3

Table for 850nm LED

SI IF in mA Power mtr reading Power mtr reading

In µW in(dBm)

1.

2.

3.

4.

Note: Convert the power meter reading from µW to dB using formula. Given below. dBm=10*log (Power meter reading in mW/1mW)

In this case, dBm=10*log(power mtr reading in µw/1000)

Conclusion: From this experiment, It will be observed that the L.E.D. at 660nm and 850 nm have a linear response for Po vs Iғ in a limited region of Iғ. By selecting this region of Iғ for operation, a linear intensity modulation system for signal transmission can be designed. EXPERIMENT 3: CHARACTERISATION OF A FIBER OPTIC PHOTO TRANSISTOR.

7

Aim of the Experiment 3.1: Aim of the experiment is to study the relationship between the optical input power on photo detector and the resultant photo current Ip. The photo detector in this case is a photo transistor.

Theory: PIN photodiodes, avalanche photo diodes and photo transistors are commonly used photo detectors used in optical communication systems. In analogue signal reception, where intensity modulated light signal is to be received and demodulated to give an electrical output, the linearity of the device is of paramount importance. The relationship Between photo transistor photo current Ip and the optical Power (Pin) input at a given wavelength is given by Ip=Q.Pin Where Q is a constant.

Experiment Procedure: 1. Short the M2 of I .R LED (+ve and –ve terminals) of Tx Unit and Connect the photo transistor output terminals of Rx unit to M1 volt meter on Tx Unit as shown on fig 3.1, 2. Connect one end of OF cable1 to the 850nm L.E.D. FC adaptor of Tx unit and the other end to PIN diode FC adaptor, Move the S1 switch on Tx unit towards 850nm IR

L.E.D. and Then turn on the AC mains.

3. Set the carrier power Po to approx,3µW value. 4. Remove the cable from PIN diode FC adaptor and Connect to Photo transistor FC

adaptor of Rx unit. 5. Rotate the Rin pot to the extreme clock wise direction to get minimum gain. Now

note down the Vout on the volt meter provided on Tx unit. 6. Photo transistor current can be calculated as Ip = Vout / (Rin*G). Where G is the

internal gain of the amplifier.

Hence G = For 660nm L.E.D. and G = For 850nm L.E.D. 7. Repeat the above steps by increasing in steps 3µW of Po values. And tabulate

the readings in table 3.1. Entire experiment can be repeated for 660nm L.E.D, during this S1 switch should be moved towards 660nm red L.E.D. throughout the experiment.

V660nm PT

OF Cable S1

850nm Pin PM

M2

Fig 3.1

8

Table 3.1:

Table for 850nm LED

SI Power meter P0 Vout Ip=Vout/Rin*G

NO. Reading in µW in (dBm) in Volts

1.

2.

3.

4.

5

Table 3.2:

Table for 660nm LED

SI Power meter P0 Vout Ip=Vout/Rin*G

NO. Reading in µW in (dBm) in Volts

1.

2.

3.

4.

5

Note: Convert the power meter reading from µW to dBm using formula. Given below :

dB=10*log(power mtr reading in µw/1000)

Conclusion: It will be observed from the above results that for the both 660nm and 850nm wavelengths the Photo transistor responds linearly to the optical input over wide range of Iғ values.

9

EXPERIMENT 4 : DESIGN AND STUDY OF A LINEAR INTENSITY MODULATION SYSTEM FOR ANALOGUE TRASMISSION.

Aim of the experiment 4.1: The aim of the experiment is to study the following AC characteristics of linear intensity modulation systems. (a). Gain characteristics of a Fo Linear intensity modulation system Vin(ac) vs. Vout(ac) for fixed carrier power Po and signal frequency fo.

(b). Frequency Response of a Fo Linear Intensity Modulation System Vout (ac) vs. Fo at fixed carrier power Po and Vin(ac)

(c). Waveform distortion in a Fo Linear intensity Modulation system Vin(ac)(Max)vs. P0 at fixed Fo.

(d) Gain bandwidth product of a Fo linear intensity modulation receiver Gain vs. Band width for fixed Vin.

Experiment Procedure (4a):: Gain characteristics of a Fo Linear intensity modulation system Vin(ac) vs. Vout(ac) for fixed carrier power Po and signal frequency fo. With the Use of external dual trace CRO.

1. Connect the Sine wave frequency generator output terminals to the Vin and ground

terminals of the Tx unit using patch cords, Short the M2 of IR LED ( +ve and –ve terminals ) on the Tx Unit. 2. Connect one end of cable 1 to the 850nm L.E.D. FC adaptor of Tx unit and the other

end to PIN diode FC adaptor of Rx unit and fix the carrier power Po at 5µW. 3. Remove FC connector from PIN diode FC adaptor and connect it to Photo

Transistor FC adaptor. 4. Connect the CH1 ( Channel 1 ) of CRO across the Vin +ve and Gnd terminal of the Tx

unit. And CH2 ( Channel 2 ) of CRO across the CRO inputterminals of the Rx unit. As shown in fig.4.1(a) 5. Fix the input frequency at 500Hz using frequency setting pot on Tx unit from the sine

wave generator. 6. Now Increase the amplitude of the input signal in steps of 100mV, and

note the input and output signals Peak to Peak voltages on the CRO.

7. Tabulate the readings in Table 4.1

10

Fig 4.1(a)

Tx Unit Rx Unit

660nm PT

fin vin 850nm OF Cable

Pin

amp gnd M2 PM CRO

Table 4.1

Fo=2KHz,P0=1µW

SI Vin(mVp-p) Vout(mVp-p) Gain=Vout/Vin

No

1.

2.

3.

4.

5.

11

Experiment Procedure(4b):

Frequency Response of a FO ( Fiber Optic ) Linear Intensity Modulation System, Vout (ac) vs. Fo(out put frequency) at fixed carrier power Po and Vin(ac) With the Use of external dual trace CRO.

1. Connect the frequency generator output terminals to the Vinput and ground terminals of the Tx unit using patch cords, Short the M2 of IR LED ( +ve and –ve terminals ) of Tx Unit. 2. Connect one end of cable 1 to the 850nm L.E.D. FC adaptor of Tx unit and the other end

to PIN diode FC adaptor of Rx unit and fix the carrier power Po at approx. 10µW. 3. Remove FC connector from PIN diode FC adaptor and connect it to Photo

Transistor FC adaptor. 4. Connect the CH1 ( Channel 1 ) of CRO across the Vin +ve and Gnd terminal of the Tx

unit. And CH2 ( Channel 2 ) of CRO across the output and Gnd terminals of the Rx unit. As shown in fig.4.1(a)

5. Now fix input signal amplitude Vin(ac) at 500mv.

6. Increase the Frequency of the input signal in suitable steps of 100hZ.

and note the input frequency and output signal Vout Peak-Peak voltage on the CRO channel 1 and channel 2 respectively.

7. Tabulate the readings in Table 4.2.

Table 4.2

P0=1µW; Vin (ac) =-500mVp-p

SI fo(Hz ) Vout SI F0(Hz) Vout(mv)

No. (Vp-Vp) No.

1. 100 6. 1000

2. 200 7. 1500

3. 300 8. 2000.

4. 400 9. 2500.

5. 500 10. 3000

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Experiment Procedure(4c): Waveform distortion in a FO Linear intensity Modulation system Vin(ac)(Max)vs. P0 at fixed FO. With the use of dual trace CRO.

STEP 1: Connect the frequency generator output terminals to the Vin and ground terminals of the Tx unit using patch cords, Short the M2 of IR LED +ve and –ve terminals of Tx Unit. STEP 2: Connect one end of cable 1 to the 850nm LED FC adaptor of Tx unit and the other end to PIN diode FC adaptor of Rx unit and fix the carrier power Po at 5µW. STEP 3: Remove FC connector from PIN diode FC adaptor and connect it to Photo Transister FC adaptor. STEP 4: Connect the CH1 of CRO across the Vin +ve and Gnd terminal of the Tx unit. And CH2 of CRO across the output and Gnd terminals of the Rx unit. As shown in fig.4.1(a) STEP 5: Fix the input frequency at 800Hz using frequency setting pot on Tx unit. STEP6:Now increase Vin(ac) gradually from 10mv(p-p) and Observe Vout on the oscilloscope. Note the reading of Vin(p-p)max for which distortion sets in output voltage Vout(p-p). Repeat this for other values of P0. STEP 7: Tabulate the readings in Table 4.3. Table 4.3.

Frequency fo=800Hz

SI.N0 Po(1µW) Vin(Vp-p) max

1. 5µW

2. 10µW

3. 15µW

4. 20µW

Experiment Procedure4(d):

Gain bandwidth product of a FO ( Fiber Optic ) linear intensity modulation receiver Gain vs Band width for fixed Vin.

1. Connect the Sine wave frequency generator output terminals to the Vin and ground

13

terminals of the Tx unit using patch cords, Short M2 of IR LED( +ve and –ve terminals

) on Tx Unit with patch chords. 2. Connect one end of cable 1 ( 1 meter ) to the 850nm L.E.D. FC adaptor of Tx unit and

the other end to PIN diode FC adaptor of Rx unit and fix the carrier power Po at approx. 10µW.

3. Remove FC connector from PIN diode FC adaptor and connect it to Photo Transistor FC adaptor.

4. Connect the CH1 ( Channel 1 ) of CRO across the Vin +ve and Gnd terminal of the Tx unit. And CH2 ( Channel 2 ) of CRO across the output and Gnd terminals of the Rx unit. As shown in fig.4.1(a)

5. Now Fix input signal amplitude Vin(ac) at 500mv. 6. Increase the Frequency of the input signal to 800Hz observe the transmitted Vin and

Received Vout signals on the oscilloscope. Set the Rin such that the gain (Vout/Vin)=1.0. Repeat the experiments for other gains(2,3,4 etc) and note the input, output signal Pk-Pk voltages on the CRO channel 1 and channel 2 respectively.

7. Tabulate the readings in Table 4.4.

Table 4.4

Fin=800Hz,Vin(ac)=500mV,P0=5µW.

SI.N0 Gain Vin(Vp-p)

1. 0.25

2. 0.5

3. 1.0

.

4 2

5. 3

14

EXPERIMENT 5: DETERMINATION OF NUMERICAL APERTURE OF OPTICAL FIBERS

Aim of the Experiment : The aim of the experiment is to determine the numerical aperture of the optical fibers available.

Theory: Numerical aperture of any optical system is a measure of how much light can be collected by the optical system. It is the product of refractive index of the incident medium and sine of the maximum ray angle.

NA=ni.sinӨmax ni for air is 1, Hence NA=

NOTE: In this particular experiment connections to Voltmeter (M1), Ammeter(M2),Signal generator are not required. Connect the circuit as mentioned below

Experiment Procedure:

The experimental set up for numerical aperture measurement system is as shown in below figure 5.1.

AC mains NA Jig

Tx unit

Set P0

Fig 5.1

1. Connect one end of the cable one to the 660nm L.E.D. FO connector of Tx Unit and

other end to the NA jig as shown in the above figure 5.1. 2. Plug the AC mains Turn the Po knob to clockwise direction to set maximum P0.

The light intensity should increase at the end of the fiber on the NA Jig.

3: Hold the white scale-screen, provided in the Kit vertically at a distance of 15mm(L) from the emitting fiber end and view the red spot on the screen (A dark room is necessary to facilitate a good contrast).

Now measure the maximum diameter(W) of the spot.

4. Compute NA from the formula NA = sinӨmax = W / (4L²+W²)½, Repeat the experiment at 10mm, 20mm an d 25mm distances and tabulate the readings in the table 5.1

15

Table 5.1

SI N0 L (mm) W(mm) NA Ө(degrees)

1.

2.

3.

4.

5.

Specifications of PMMA Fiber optic cable

16