Engineering Physics Laboratory Manual cum Record ...

Engineering Physics Laboratory

Manual cum Record

DEPARTMENT OF PHYSICS

GOKARAJU RANGARAJU

INSTITUTE OF ENGINEERING AND TECHNOLOGY

(Autonomous)

Bachupally, Hyderabad – 500 090

Preface

The main objective of the laboratory manual entitled “Engineering Physics laboratory manual” is

to make the first year B. Tech students familiar with the physics lab in a more systematic manner. This

manual is written according to GRIET (Autonomous) syllabus .This book has been prepared to meet the

requirements of Engineering Physics lab.

This book is written and verified by the faculty of Department of Physics.

1. Dr. G. Patrick, Professor

2. Dr. M. Sridhar, Professor

3. Dr. K. Vagdevi, Associate professor

4. Dr. J. Kishore Babu, Assistant Professor

5. Mr. M. Krishna, Assistant Professor

6. Ms. B. Shanti Sree, Assistant Professor

7. Ms. G. Kalpana, Assistant Professor

GOKARAJU RANGARAJU

INSTITUTE OF ENGINEERING AND TECHNOLOGY

(Autonomous)

CERTIFICATE

This is to certify that this is a bona fide record of practical work done by

_____________________________________________________________ of

I B.Tech (I / II Semester) Reg. No.______________________________ in the

Engineering Physics Laboratory during the academic year ________________

Faculty In charge External Examiner

Gokaraju Rangaraju Institute of Engineering& Technology

(Autonomous)

GR20A1013: ENGINEERING PHYSICS LAB

(Common to CE and ME)

B. Tech I Year L: 0 T: 0 P: 3 C: 1.5

Course objectives: At the end of the course the student is expected to

• Experiment with resonance phenomena using mechanical and electrical sources

• Analyze the mechanical properties of solid materials.

• Recall the basic properties of light through hands on experience.

• Apply the theoretical concepts of optical fibers in practical applications.

• Outline the characteristics of various semiconducting materials.

Course outcomes: At the completion of this course, students will be able to:

• Estimate the frequency of tuning fork, spring constant through coupled oscillation and

analyze the resonance phenomena in LCR circuit.

• Compare the rigidity modulus of wires of different materials using Torsional pendulum.

• Interpret the properties of light like interference and diffraction through experimentation.

• Asses the characteristics of Lasers and infer the losses in optical fibers.

• Identify the type of semiconductor by measuring energy gap.

INDEX

S:NO Name of The Experiment Page No

1 Melde’s experiment: To determine the frequency of a turning fork using

Melde’s arrangement.

2 Torsional pendulum: To determine the rigidity modulus 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 wavelength of the light source by

using diffraction 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 the resonant frequency and quality factor of

LCR circuit in series and parallel.

8 LASER: To study the V-I and P-I characteristics of LASER sources.

9 Optical fiber: To determine the Numerical aperture and bending losses of

Optical fibers.

10 Energy gap of P-N junction diode: To determine the energy gap of a

semiconductor diode.

1 .MELDE’S EXPERIMENT – TRANSVERSE AND LONGITUDINALMODES.

AIM: - To determine the frequency of a turning fork using Melde’s arrangement.

APPARATUS: An electrically maintained tuning fork ,a light smooth pulley fixed to a

stand, a light scale pan, thread, battery eliminator, rheostat, plug key and connecting wires.

FORMULA: Transverse mode ɳ = 1

2𝑙√

𝑇

𝑚 =

1

2√𝑚 √𝑇

𝑙 𝐻𝑧

Longitudinal Mode ɳ = 1

𝑙√

𝑇

𝑚=

1

√𝑚 √𝑇

𝑙 𝐻𝑧

Where m=Linear density (Mass per unit length)

T=Tension = (M+P) g

M=Load applied in to the pan

P=Mass of the pan

g=Acceleration due to gravity

l=Length of each loop

DESCRIPTION: When a string under tension is set into vibrations, transverse harmonic waves

propagate along its length. When the length of string is fixed, reflected waves will also exist. The

incident and reflected waves will superimpose to produce transverse stationary waves in the

string.

The string will vibrate in such a way that the clamped points of the string are nodes and

the point of plucking is the antinodes.

A string can be set into vibrations by means of an electrically maintained tuning fork,

thereby producing stationary waves due to reflection of waves at the pulley. The loops are

formed from the end of the pulley where it touches the pulley to the position where it is fixed to

the prong of tuning fork.

Melde’s apparatus can be arranged in two modes of vibration,

TRANSVERSE MODE

When the direction of motion of the prong is at right angles to the length of the string, the

vibrations of the thread represent the transverse mode of vibration.

FOR TRANSVERSE ARRANGEMENT

LONGITUDINAL MODE

When the direction of motion of the prong is along the length of the thread, the vibrations of

the thread represent longitudinal mode of vibration.

FOR LONGITUDINAL ARRANGEMENT:

ɳ = 1

2𝑙√

𝑇

𝑚 =

1

2√𝑚 √𝑇

𝑙 𝐻𝑧

ɳ = 1

𝑙√

𝑇

𝑚 =

1

√𝑚 √𝑇

𝑙 𝐻𝑧

PROCEDURE FOR TRANSVERSE MODE:

1. Find the weight of pan P and arrange the apparatus as shown in figure.

2. Place a load of 4 To 5 gm in the pan attached to the end of the string

3. Passing over the pulley. Excite the tuning fork by switching on the power supply.

4. Adjust the position of the pulley so that the string is set into resonant

5. Vibrations and well defined loops are obtained. If necessary, adjust

6. The tensions by adding weights in the pan slowly and gradually increase. For finer

adjustment, add milligram weight so that nodes are reduced to points.

7. Measure the length of say 4 loops formed in the middle part of the string. If ‘L’ is the

distance in which 4 loops are formed, then distance between two consecutive nodes is

L/4.

8. Note down the weight placed in the pan and calculate the tension T.

9. Tension, T= Mg

10. Repeat the experiment twice by changing the weight in the pan in steps of one gram and

altering the position of the pulley each time to get well defined loops.

11. Measure one meter length of the thread and find its mass to find the value of m, the mass

produced per unit length.

12. Adjust the apparatus for longitudinal arrangement and repeat the same procedure.

OBSERVATION AND CALCULATION:

FOR TRANSVERSE ARRANGEMENT

Linear density (mass per unit length) m = Total mass of the thread

Total length of thread = ……… gm/cm

Mass of the pan, P=…………………gm

S:NO Load

applied

(M) gm

Tension

T=(M+P)g

gm

Number of

Loops(x)

cm

Length of

thread(y)

cm

Length of

each loop

(l=y/x)

√𝑇 √T

𝑙

1

2

3

4

5

Frequency ɳ = 1

2𝑙√

𝑇

𝑚 =

1

2√𝑚 √𝑇

𝑙 𝐻𝑧 = ……………….Hz

FOR LONGITUDINAL ARRANGEMENT:

Linear density (mass per unit length) m = Total mass of the thread

Total length of thread = ……… gm/cm

Mass of the pan , P =…………………gm

S:NO Load

applied

(M) gm

Tension

T=(M+P)g

gm

Number of

Loops(x)

cm

Length of

thread(y)

cm

Length of

each loop

(l=y/x)

√𝑇 √T

𝑙

1

2

3

4

5

Frequency ɳ = 1

𝑙√

𝑇

𝑚 =

1

√𝑚 √𝑇

𝑙 𝐻𝑧 =…………………Hz

RESULT:

The Frequency of electrically driven Tuning fork in Transverse arrangement = Hz

The Frequency of electrically driven Tuning fork in Longitudinal arrangement = Hz

VIVA-VOCE:

1. What do you mean by Frequency?

Number of vibrations per second.

2. Define Resonance?

Vibrating a body with its natural frequency under the influence of another vibrating body

is called resonance.

3. Difference between transverse wave and longitudinal wave?

In a transverse wave the particle vibrate perpendicularly where as in longitudinal wave

the particle vibrate parallel with respect to the direction of propagation of a wave.

4. What is standing wave?

Standing wave is superposition of propagating waves that have same amplitudes and

frequencies but traveling in opposite directions. The term standing or stationary refers to

the fact that the nodes and antinodes of the wave remain fixed in position.

2. TORSIONAL PENDULUM – RIGIDITY MODULUS

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

APPARATUS: Torsional pendulum, stop watch, screw gauge, vernier calipers, scale

FORMULA: Rigidity modulus ɳ = ( 8𝜋

2 ) (

𝑀𝑅2

𝑎4 ) ( 𝐿

𝑇2)

Where M = Mass of the disc

R = Radius of the disc

a = Radius of the wire

L = Length of the wire

T = Time period

DESCRIPTION: Torsional Pendulum consists of a uniform metal disc (or cylinder)

suspended by a wire whose rigidity modulus is to be determined. The lower end of the wire is

gripped in a chuck fixed at the center of the disc and the upper end is gripped in another

chuck fixed to a wall bracket as shown in the fig.

The disc is turned through a small angle in the horizontal plane to oscillations about the axis

of the wire. The period of oscillations given by

T= 2𝜋√𝐼

𝐶 (i)

Where I is the moment of inertia of the disc about the axis of rotation and C is the couple per

unit twist of the wire.

But C = 𝜋 ɳ 𝑎4

2𝑙 (ii)

Where a is the radius of the wire L is its length and ɳ is the rigidity modulus. From (i) and

(ii) we have

ɳ =8𝜋𝐼

𝑎4

𝐿

𝑇2 (iii)

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

rotation of the moment of inertia I is given by

I = 𝑀𝑅2

2

Where M is the mass of the disc and R is the radius .On substituting the value of I in the Eqn.

(iii) we get

ɳ = 8𝜋

2 𝑀𝑅2

𝑎4

𝐿

𝑇2 (iv)

PROCEDURE:

1. A meter wire whose ‘ɳ’ is to be determined is taken without any kinks. The disc is

suspended from one end of the wire .The other end of the wire is passed through the

chuck fixed to the wall bracket and is rigidly fixed.

2. The length ‘L’ of the wire between the chucks is adjusted to a convenient value (say 50

cms). A pin is fixed vertically on the edge of the disc and a vertical pointer is placed in

front of the disc against the pin to serve as a reference to count the oscillations.

3. The disc is turned in the horizontal plane through a small angle, so as to twist the wire

and released. There should not be any up and down and lateral movements of the disc.

4. When it is executing Torsional oscillations, time for 20 oscillations is noted twice and the

mean is taken. The period (T) is then calculated 1/𝑇2.

5. The experiment is repeated for different values of ‘L’ and in each case the period is

determined. The value of L/ 𝑇2 is calculated for each length. The observations are

tabulated.

6. From the observations mean the value of L/𝑇2 is calculated. The mass ‘M’ of the disc is

measured with a physical balance and its radius ‘R’ is calculated with Vernier calipers.

7. The radiuses of the wire ‘a’ is determined very accurately with screw gauge at three of

four different places and mean value is taken since it occurs in fourth power.

8. Substituting these values in eqn (iv) ‘ɳ’ is calculated. A graph is drawn taking the

value‘L’ on the ‘x’ axis and the corresponding values of 𝑇2 on the Yaxis.

9. It is a straight line graph passing through origin. Slope can be calculated from the graph

by inverting the slope we will get L/𝑇2 Substituting this value ‘ɳ’ is calculated.

OBSERVATIONS:

Least count of vernier calipers

𝐿𝐶 = 1MSD

n =

1Main Scale Division

Total no.of divisions in vernier scale

Least count of screw gauge

𝐿𝐶 = 1 PSD

n =

1 Pitch Of the screw

Total no.of divisions on head scale

DETERMINATION OF RADIUS OF DISC

S.No. MSR(cm) VSR(cm) D = MSR +VSR×LC (cm)

Diameter of disc D =

Radius of disc /2 =

DETERMINATION OF RADIUS OF WIRE (a)

S.No. PSR (mm) HSR (mm) Corrected HSR a = PSR +( HSR×LC) mm

Diameter of Wire a =

Radius of Wire a

2 =

Least count of Vernier calipers (L.C) = ------------------cm

Least count of Screw gauge (L.C) = ------------------cm

Average radius of the wire (a) = ------------------------cm

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

Mean radius of the disc (R) = ------------------------------cm

TABLE TO FIND TIME PERIOD

S.No Length L (cm) Time for 20 oscillations Time Period

T=Meantime/20 𝑇2

(S2 )

𝑙

𝑇2

Cm s-2 Trail I Trail II Mean

time

Mean value of 𝑙

𝑇2 =

CALCULATIONS:

ɳ = ( 8𝜋

2 ) (

𝑀𝑅2

𝑎4 ) ( 𝐿

𝑇2)

Model Graph:

A graph is drawn between L and 𝑇2

RESULT:

Rigidity modulus (ɳ) of the wire -----------------dynes/cm2

VIVA VOCE:

1. What is Torsional pendulum?

Body suspended from a rigid support by means of a long and thin elastic wire is called

Torsional pendulum.

2. What is the type of oscillation?

This is of simple harmonic oscillation type.

3. On what factors do the time period depends?

It depends upon I) moment of inertia of the body II) rigidity of wire i.e., length, radius

and material of the wire.

4. How will you determine the rigidity of fluids?

As fluids do not have a shape of their own, hence they do not posses rigidity. Hence

there is no question of determining.

5. Define Rigidity modulus?

When tangential surface forces are applied on a body, the successive layers of the

material are moved or sheared. This type of strain is called shearing strain. “The ratio of

tangential stress to shearing strain is called Rigidity of modulus.

Rigidity of modulus= Tangential stress / shearing strain.

Tangential stress = Force/Area.

Shearing strain= θ

6. Define Moment Of Inertia?

It is the measure of the inertia of a body in rotatory motion. It depends upon the

axis of rotation, mass of the body and also on the distribution of the mass about the axis.

7. What is the meaning in calling this a pendulum?

The disc is making oscillations around a vertical axis passing through its centre of

mass and hence the arrangement is called a Torsional pendulum.

8. Difference between simple pendulum and Torsional pendulum?

In a simple pendulum the Simple harmonic motion is due to the restoring force

which is the component of the weight of the bob. In a Torsional pendulum the Simple

Harmonic motion is due to the restoring couple arising out of torsion and shearing

strain.

9. What is S.H.M?

A body is said to have a S.H.M, if its acceleration is always directed towards a fixed

point on its path and is proportional to its displacement from the fixed point.

10. What is Young’s modulus?

It is the ratio of longitudinal stress to the longitudinal strain.

11. Define Time Period?

Time taken for one complete oscillation.

SPACE FOR GRAPH SHEET

3. NEWTON’S RINGS - RADIUS OF CURVATURE OF PLANO CONVEX LENS.

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

APPARATUS: Travelling microscope, sodium vapour lamp, Plano-convex lens, plane glass

plate, magnifying lens.

FORMULA

R = 𝐷𝑛

2− 𝐷𝑚2

4𝜆(𝑛−𝑚) 𝐴𝑜

R = Radius of curvature of Plano convex lens

Dn = Diameter of nth ring

Dm = Diameter of mth ring

λ = wave length of sodium vapour lamp

INTRODUCTION:

The phenomenon of Newton’s rings is an illustration of the interference of light waves reflected

from the opposite surfaces of a thin film of variable thickness. The two interfering beams,

derived from a monochromatic source satisfy the coherence condition for interference. Ring

shaped fringes are produced by the air film existing between a convex surface of a long focus

Plano-convex lens and a plane of glass plate.

DESCRIPTION: The convex lens is placed on the optically plane plate B as shown in the

below fig. on the platform of the traveling microscope. A black paper is placed under the

glass plate.

The condensing lens C is placed at a distance equal to the focal length of the lens from the

sodium Vapor lamp. The emergent parallel beam of the light is directed towards the glass

plate ‘A’ kept directly above the center of the lens and inclined at 450 to the vertical. The

beam of light is reflected on the lens ‘L’. As a result of interference between the light

reflected from the lower surface of the lens and the top surface of the glass plate B, Newton’s

rings with alternate bright and dark rings are formed having a black center. The microscope

can focus these rings. (It may happen that the center of the ring system is bright. This is due

to the presence of dust particles between the lens and the thick glass plate. In such a case the

surface of the lens and the glass plate has to be cleaned.)

PROCEDURE:

1. Clean the plate G and lens L thoroughly and put the lens over the plate with the curved

surface below B making angle with G(see fig )

2. Switch on the monochromatic light source. This sends a parallel beam of light. This beam

of light gets reflected by plate B falls on lens L.

3. Look down vertically from above the lens and see whether the center is well illuminated.

On looking through the microscope, a spot with rings around it can be seen properly by

focusing the microscope.

4. Once good rings are in focus, rotate the eyepiece such that out of the two perpendicular

cross wires, one has its length parallel to the direction of travel of the microscope. Let

this cross wire also passes through the center of the ring system.

5. Now move the microscope to focus on a ring (say, the 10th order dark ring) on one side

of the center. Set the crosswire tangential to one ring as shown in below fig . Note down

the microscope reading.

(Make sure that you correctly read the least count of the vernier in mm units)

6. Move the microscope to make the crosswire tangential to the next ring nearer to the

center and note the reading. Continue with this purpose till you pass through the center.

Take readings for an equal number of rings on the both sides of the center.

A graph is drawn with number of the dark ring on the x-axis and the square of the diameter

(D2) on the y-axis. The graph is a straight line passing through origin. From the graph the

values of 𝐷𝑚2 and 𝐷𝑛

2corresponding to nth and mth rings are found.

The wavelength 𝜆 of sodium light is found by the formula

𝜆 = 𝐷𝑛

2− 𝐷𝑚2

4𝑅(𝑛−𝑚) 𝐴𝑜

Radius of curvature can be obtained by

R = 𝐷𝑛

2− 𝐷𝑚2

4𝜆(𝑛−𝑚) 𝐴𝑜

On taking the standard wave length of sodium light, the radius of curvature of the lens can be

calculated.

The value of the radius of the curvature of the lens is verified by using spherometer

OBSERVATIONS:

Least count of vernier of traveling microscope = ___________________mm

LC = Smallest (or) 𝑂𝑛𝑒 𝑑𝑖𝑣𝑖𝑑𝑖𝑜𝑛 𝑜𝑛 𝑚𝑎𝑖𝑛 𝑠𝑐𝑎𝑙𝑒

Total no.of divisions in vernier scale

MEASUREMENT OF DIAMETER OF THE RING

S.No

Order

of the

Ring

Microscope Reading

Diamete

r

D = R-L

D2

Left side(L) Right side(R)

MSR

VC

MSR+(VC*LC)

MSR

VC

MSR+(VC*L C)

CALCULATIONS:

R = 𝐷𝑛

2− 𝐷𝑚2

4𝜆(𝑛−𝑚) or R=

𝑠𝑙𝑜𝑝𝑒

4𝜆

MODEL GRAPH:

Plot the graph of D2 Vs n and draw the straight line of best fit.

From the slope of the graph, calculate the radius of curvature R of the plano convex lens as

Wavelength of sodium light 𝞴 = 5893 Ao

RESULT: Radius of curvature of the lens= ………….. cm

VIVA VOCE:

1. What is the basic principle of Newton’s rings experiment?

The basic principle of Newton rings experiment is Interference phenomenon.

2. Define Interference phenomena?

The phenomenon of Newton’s rings is an illustration of the interference of light waves

reflected from the opposite surfaces of a thin film of variable thickness.

3. Why are the rings circular in shape?

The air film between the plane glass plate and Plano convex lens is in circular shape.

That’s why the rings are circular in this experiment.

4. What are Newton’s Rings?

Alternate dark and bright rings with central dark spot are called Newton’s rings.

5. Why it is necessary for the light to fall normally on Plano convex lens?

For interference.

6. What is constructive interference and destructive interference?

When two light waves interfere with each other such that the resultant intensity is

maximum at a point is called constructive interference. If the resultant intensity is

minimum then that is called destructive Interference.

7. What is the purpose of glass plate to incline at 450 in this experiment?

For normal incidence of light wave.

8. Why the centre of the rings is dark?

Because the Plano convex lens and the plane lens both are in contact and at that particular

place, the centre dark ring will appear.

9. Which light do you use in this experiment?

Monochromatic light. Example: Sodium light.

10. What will happen if we use White light in this experiment?

Colored fringes will form.

11. If you replace yellow light with green light, is there any difference in the formation

of rings?

No ,because both are Monochromatic lights only.

SPACE FOR GRAPH SHEET

4. Diffraction Grating

AIM: To determine the wavelength of the light source by using diffraction grating.

APPARATUS: Spectrometer, Sodium Vapour Lamp, Plane diffraction grating, grating holder,

Spirit level and reading lens.

FORMULA: wavelength of radiation is

λ= 2×2.54×sin (

𝐷

2)

15000

λ = 2×2.54×sin (

𝐷

2)

Nn

Where D = Angle of minimum deviation

n = Order of the spectrometer and

N = No.of lines per cm on grating

DESCRIPTION OF THE SPECTROMETER: The spectrometer is used to make

measurements with the spectrum of a source of light. The essential parts of spectrometer are

Collimator

Prism Table

Telescope

COLLIMATOR: The collimator consists of a convex lens and a slit of adjustable width

mounted co-axially at the ends of metal tubes. The distance between the slit and lens can be

adjusted by a rack and pinion screw and so adjusted that the slit is at the focus of the lens. It is

fixed horizontally in a vertical plane. The slit is placed in front of source of light and the width of

the slit can be adjusted. The beam of light coming out of the collimator is a parallel beam.

PRISM TABLE: It is an arrangement to keep the prism table on. It consists of three leveling

screws. Using a spirit level it can be made horizontally can be rotated horizontally about a

vertical axis that coincides with the axis of rotation of the telescope. The position of the prism

table can be read with the help of two vernier, which move over the edge of a circular main

scale. Usually another horizontal plate called turn table is attached to it. This serves as the seat of

reflecting or refracting device. It can be leveled by screws and can be detached from the verniers

by means of side screw.

TELESCOPE: An astronomical telescope fitted with a Ramsden eyepiece is used to observe the

emergent beam of light. It is fitted horizontally to a disc that can be made horizontal by

adjustable screws at its bottom. The circular main scale divided into degrees or part of a degree is

attached to the disc carrying the telescope. It can be fixed in any position by a screw and further

be given slow motion by a tangential screw to its carrier.

PRELIMINARY ADJUSTMENTS OF THE SPECTROMETER:

EYEPIECE: The telescope is turned towards white wall and the eyepiece is moved inwards or

outwards till the set of cross wires is seen clearly through the telescope.

TELESCOPE: The telescope is turned to view a distant linear vertical object and its rock and

pinion screw is adjusted until the object is clearly seen and finally until there is no parallax

between the image of the object and that of the cross wires as the observer moves his head from

side to side. This means it is adjusted to receive parallel rays.

PRISM TABLE: A spirit level is kept on prism table parallel to the line joining any two

leveling screws. One of the screws is adjusted until the air bubble in the spirit level is at its

center. Then it is kept perpendicular to this position and third screw is adjusted so that the air

bubble is at the center. Thus the prism table is made perfectly horizontal.

After making the adjustments of the spectrometer the least count of the vernier is found by the

relation,

L.C = 𝑆

𝑁

Where S = the value of one division on circular scale (1/20)

N= the total number of divisions on venires (30)

L.C = (1/20)/30 = 10/60 = 1min

Least count of spectrometer = 1 𝑀𝑆𝐷/ 𝑁𝑜 of 𝑑𝑖𝑣 𝑖𝑛 𝑣𝑒𝑟𝑛𝑖𝑒𝑟 𝑠𝑐𝑎𝑙𝑒

DESCRIPTION: A plane diffraction grating consists of a parallel sided glass plate with

equidistant and fine parallel lines drawn very closely upon by means of a diamond point. The

number of lines drawn is about 15000 per inch (the grating used in laboratory is exact replica of

the original grating on cellulose film.)

THEORY: When light of wavelength λ is incident normally on a diffraction grating having N

lines per cm and if ϕ is the angle of diffraction in the nth order spectrum, then

nN λ = sinϴ

or λ = sinϴ

nN

or λ = sinϴ ×2.54

n ×15,000 (1 inch =2.54cm)

Again when a parallel beam of monochromatic light incident upon a grating is diffracted in such

a way that the angle of deviation is minimum; then the wavelength of radiation is given by

λ= 2sin (

𝐷

2)

nN

λ= 2×2.54×sin (

𝐷

2)

15000

Where D = angle of minimum deviation

n = the order of the spectrometer and

N = the number of lines per cm

MINIMUM DEVIATION METHOD:

The direct image of the slit is observed through the telescope. The point of intersection

of the cross wires is set on the sharp image of the slit. The vernier table is fixed and the reading

on the circular scale is noted.

The prism table is released from the vernier table. The telescope is turned to one side,(say

right) and the first order diffracted image is observed. The prism table is slowly rotated to the

right, as it is slowly rotated towards right side the image first moves towards left, reaches a

limiting position and then retraces its path. In this limiting position, the telescope is fixed such

that the point of intersection of the cross wires is on the D1 line and the reading on the circular

scale is taken. The difference between the direct readings gives the angle of minimum deviation

for the line D1 in the first order spectrum, similarly the reading gives the angle of minimum

deviation for the D2 line of the first order.

Next, the angle of minimum deviation for the D1 and D2 lines in the second order

spectrum is found similarly. The results are tabulated in the table below.

OBSERVATIONS:

L.C = (1/20)/30 = 10/60=1min

No. Of lines per cm. on the grating (N) =

Here V1= MSR+VC*LC

V2 = MSR+VC*LC

Similarly for V1’ ,V2’, V1

’’, V2’’

Direct

reading

Minimum deviation

position

Angle of minimum deviation

Dm

Mean

Dm

λ= 2sin (

D

2)

nN

Left side Right side

n V1 V2 V1, V2

, V1

,, V2

,, |𝐴 −𝐶| |𝐵−𝐷| |𝐴 − 𝐸| |𝐵 −𝐹|

A B C D E F G H I J

MEASUREMENT OF : The telescope is rotated so as to catch the first order diffracted

image on one side, say left. With sodium light two images of the slit, very close to each other can

be seen. They are called D1 and D2 lines .The point of intersection of cross wires is set on the D1

line and its reading is noted on both the vernier scales.similarly the reading corresponding to D2

line is noted. Then the telescope is turned to the other side i.e to the right side and similarly the

reading corresponding to D1 and D2 lines of the first order spectrum are note

RESULT: The wavelength of a given light using a plane diffraction grating is determined in

minimum deviation position.

D1, = ……………….cm

D2, = ……………….cm

VIVA VOCE:

1. Define Diffraction?

The phenomenon of bending of light waves around the edges of obstacles and their

spreading into the geometrical shadow of the obstacle is called diffraction of light.

2. What is grating?

A grating is a plane glass plate on which a large number of opaque rulings are drawn at

equidistance with a diamond head.

3. Describe essential parts of spectrometer?

Collimator , prism table, telescope.

4. Why do we need two vernier scales?

To remove the error in reading due to coinciding the axis of prism table and telescope.

5. Why does red color deviate the most in case of grating?

This is so because in case of grating sin θ=n λ/(e+d) i.e angle of diffraction is

proportional to the wavelength and the wavelength of red is maximum.

6. Mention the two types of diffraction?

i) Frenels diffraction

ii) Fraunhofer diffraction

What is the type of diffraction in the diffraction grating experiment?

Fraunhofer diffraction is involved because the source and the screen are effectively at infinite

distance.

5. DISPERSIVE POWER OF THE MATERIAL OF A PRISM –SPECTROMETER

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

APPARATUS: Spectrometer, Prism and Mercury Vapour Lamp

FORMULA: The Dispersive power of the material of the given prism is

Where 𝜇1and 𝜇2are refractive indices of two colors

μ = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑣𝑎𝑐𝑐𝑢𝑚

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑎𝑖𝑟 =

𝜇1+𝜇2

2

𝜇 =sin 𝑖

sin 𝑟 =

𝐬𝐢𝐧 (𝐀 +𝑫𝒎

𝟐)

𝐬𝐢𝐧𝐀

𝟐

A = Angle of Prism = 600

Dm = angle of minimum deviation

THEORY: To obtain pure spectrum by spectrometer the following adjustments must be made

The axis of the telescope and that of collimator must intersect the central axis of rotation of

telescope.

The prism table is leveled with the help of spirit level.

The slit of the collimator is made narrow, vertical and symmetrical on both sides. Note the least

count of vernier scales.

𝜔 =𝜇2 − 𝜇1

𝜇 − 1

ADJUSTMENT OF THE TELESCOPE.

i) Turn the telescope towards a white wall and the distance between its objective and the

eyepiece is so adjusted that the field of view becomes completely luminous. Now the eyepiece is

displaced inside the tube till the cross-wire becomes distinctly visible.

ii) Now the telescope with objective is directed towards a distant tree or pole and they are

viewed through the telescope. The distance between the objective and the eye piece is adjusted

with the help of rack and pinion arrangement such that a distinct and clear image of the object is

seen. Thus the telescope is ready to focus all the parallel rays at the cross wire.

ADJUSTMENT OF COLLIMATOR:

Place the mercury lamp in front of the slit of collimator and align the telescope with the

collimator such that the image of the slit is seen through telescope. The distance between the slit

and the lens of the collimator is adjusted with the help of its rack and pinion arrangement until a

distinct image is seen through the telescope. In this position the light rays coming out of the

collimator will be parallel to each other.

ADJUSTMENT OF PRISM TABLE: The height of the prism table is adjusted in such a way

that the maximum light rays coming out of the collimator fall on the refracting surface of the

prism when it is placed on the prism table.

PROCEDURE:

1. The usual adjustments of the spectrometer are made. The refractive angle of the Prism is

found.

2. Then the prism is mounted on the prism table and the position of prism is adjusted to observe

the spectrum of the mercury vapor.

3. Observing the blue line in the spectrum through the telescope, the prism is adjusted for

minimum deviation position.

4. Working with the tangent screw of the telescope, the position of the prism is adjusted so that

the blue line is just one point of refracting its path after coming to the point of intersection of the

cross wires.

5. The readings of the telescope for the minimum deviation of red line are noted.

6. The telescope is brought in line with the collimator and removing the prism, the direct

readings on both vernier is noted.

7. The respective differences give the minimum deviations for blue and red colors.

OBSERVATION TABLE:

For angle of the prism: A = 600

The observations of the above experiment are as follows V1 = MSR+ (LC’) VC

L.C = 𝑆

𝑁

Where S = the value of one division on circular scale (1/20)

N= the total number of divisions on vernier (30)

L.C = (1/20)/30 = 10/60=11

Spectral Line (or)

Colour

Direct Reading Minimum Deviation Position

Angle of Min. Deviation

𝜇 =sin (

A + 𝐷𝑚 2 )

sinA2

LHS V1

RHS V2

LHS 𝑉′1

RHS 𝑉′2

Dm (LHS) |𝑉1 − 𝑉′1|

Dm (LHS) |𝑉2 −𝑉′2|

AVG Dm

Dispersive power = 𝜔 =𝜇2−𝜇1

𝜇−1

RESULT: The Dispersive power of the material of the prism = ----------------

VIVA VOCE:

1. What is the use of collimator in the spectrometer?

The collimator makes the light rays coming from the light source parallel to each other.

2. Why are lines and circles drawn on the prism table?

For placing the grating or prism properly on the prism table.

3. Why do you take readings from both the vernier?

This is done in order to eliminate the error arising due to non coincidence of the axis of

rotation of the prism table or the telescope with the centre of the circular main scale.

4. What is prism?

Transparent medium like glass bounded by two smooth surfaces which are transparent

and one rough surface which is not transparent.

5. What u meant by Angular Dispersion?

the difference in deviation between any two colors.

6. Dispersive power of the prism?

The ability to disperse various colors of the light.

7. What is Refractive index?

The ratio of sine of angle of incidence in the first medium to the sine of angle of

refraction in the second medium.

8. What is Spectrometer?

It is an optical instrument which is used to study the nature of light. It consists of

collimator, prism table and telescope.

9. What is the function of Collimator?

It will produce parallel beam of light.

10. What u meant by Angle of Prism?

Angle between two refracting surfaces of the prism.

11. What is Dispersion of Light?

When the light is allowed to fall on one of the refracting surfaces of a prism , it is split

into its constituent colours. This splitting of light into its constituent colors by refraction

through prism is called Dispersion of light.

12. What is the main optical action of the prism?

The main optical action of a prism is to disperse white light into its component parts.

Dispersion of light is minor optical action of prism, but main effect of a prism is to

deviate a beam of light.

13. What type of prism do you use in this experiment?

Crown prism.

14. What are the units of Dispersive power?

No units.

15. What type of light do you use in this experiment?

White light.

6.COUPLED OSCILATOR

AIM: To determine the spring constant by single coupled oscillator.

APPARATUS: Two compound pendulums, support stand, coupling spring and stop clock.

FORMULA: Spring constant (K) = 𝑆𝑙𝑜𝑝𝑒∗𝑚∗𝑔∗𝑙

2 Dynes/cm

Where Slope = 𝑦2−𝑦1

𝑥2−𝑥1 ( from graph)

m = Mass of each pendulum = mb+mr

mb = Mass of the bob

mr = Mass of the rod(string)

g = Acceleration due to gravity

L = Length of each pendulum = mr(

𝐿𝑅2

)+mb(Lb)

mb+mr

Lr = Length of rod(string)

Lb = Length of bob

INTRODUCTION: Two identical compound pendulums are coupled by means of a spring.

Normal mode oscillations are excited and their frequencies are measured.

The response of a system to small deformations can usually be described in terms of individual

oscillators making up the system. However, the oscillators will not have independent motion but

are generally coupled to other oscillators. Think for example of vibrations in a solid. A solid can

be thought of as being composed of lattice of atoms connected to each other by springs. The

motion of each individual atom is coupled to that of its neighboring atoms.

The description of a system of coupled oscillator can be done in terms of its normal modes. In a

coupled system the individual oscillators may have different natural frequencies. A normal mode

motion of the system however will be one in which all the individual oscillators oscillate with the

same frequency (called the normal mode frequency) and with definite phase relations between

the individual motions. If a system has n degrees of freedom (i.e. has n coupled oscillators) then

there will be n normal modes of the system. A general disturbance of the system can be

described in terms of a superposition of normal mode vibrations. If a single oscillator is excited,

then eventually the energy gets transferred to all the modes.

In this experiment we will study some of the above features in the simple case of two coupled

compound pendulums. The system studied in the experiment consists of two identical rigid

pendulums, A and B. A linear spring couples the oscillations of the two pendulums. A schematic

diagram of the system is given in Figure 1.

The motion of the two pendulums A and B can be modeled by the following coupled differential

equations (θA and θB are the angular displacements of A and B, I their moments o

Fig.1

The equations of motion of the two physical pendulums are easily obtained. Let θA and θB be

the angular displacements, and xA and xB the linear displacements of the two pendulums

respectively. The compression of the spring will be L

)xx( BA

− where is the distance

between the point of suspension and the point where the spring is attached and L the length of

the pendulum. The rotational equation for pendulum A will thus be

,cosL

)x-k(x-sinmgLdt

dI ABAACM2

A

2

−= (1)

where, the first term on the right is the restoring torque due to gravity (LCM being the distance

between the point of suspension and the position of the center of mass of pendulum A) while the

second term that due to the spring force. Assuming the mass attached to pendulum A to be

sufficiently heavy we can equate LCM and L. We also consider small displacements θA, so that

sinθAθA and cosθA 1. Substituting θA = xA/L and using the above approximations, we obtain

the following equation of motion for the linear displacement xA:

xA xB

( )I

xxkxI

mgL

dt

xd 2

BAA2

A

2 −−

−= (2)

Likewise the equation for xB is

( )I

xxkxI

mgL

dt

xd 2

BAB2

B

2 −+

−= (3)

Equations (2) and (3) are coupled, i.e. the equation for xA involves xB and vice-versa. Without

the coupling, i.e. in the absence of the spring, xA and xB would be independent oscillations with

the natural frequencyI

mgL2

0 = .

It is easy to find uncoupled equations describing the normal modes of the system. Define the

variables

x1 = xA + xB ; x2 = xA−xB (4)

Adding and subtracting eqs. (2) and (3) we obtain equations for the variables x1 and x2 as

12

1

2

xI

mgL

dt

xd

−= (5)

2

2

22

2

2

xI

k2x

I

mgL

dt

xd −

−= (6)

Note that the equations for x1 and x2 are uncoupled. The variables x1 and x2 describe

independent oscillations and are the two normal modes of the system. The general solution to

these equations will be

x1(t) = A1 cos(1t + 1) ; x2(t) = A2 cos(2t + 2) (7)

(A1, A2 being the amplitudes of the two modes and 1, 2 arbitrary phases). The corresponding

natural frequencies are the normal mode frequencies:

mgL

k21

I

k2;

2

0

22

0201

+=+== (8)

whereI

mgL0 = is the natural frequency of each uncoupled pendulum.

It is instructive to visualize the motion of the coupled system in these normal modes. If we

excite only the first normal mode, i.e. x1(t)0, but x2(t)=0 at all times, the individual motions of

pendulums A and B will be

( ) ( ) ( ) ( ))t(x)t(x2

1txtωcos

2

A)t(x)t(x

2

1)t(x 21B11

121A −==+=+= (9)

Note that in this mode xA = xB. This describes a motion in which both pendulums move in phase

with the same displacement and with frequency 1.

On the other hand if the second mode is excited, i.e. x1(t)=0 for all times and x2(t)0 the

individual motions are

( ) ( ) ( ) ( ))t(x)t(x2

1-txtωcos

2

A)t(x)t(x

2

1)t(x 21B22

221A −=−=+=+= (10)

In this mode the displacements of the pendulums are always opposite (xA(t)=−xB(t)). Their

motions have the same amplitude and frequency (=2) but with a relative phase difference of .

Figure 2 shows the motions in the normal modes.

1st normal mode 2nd normal mode

Fig.2

A general motion of the coupled pendulums will be a superposition of the motions of the two

normal modes:

( ) ( ) 222111A tωcosAtωcosA2

1)t(x +++=

( ) ( ) 222111B tωcosAtωcosA2

1)t(x +−+= (11)

For a given initial condition the unknown constants (two amplitudes and two phases) can be

solved. Consider the case where the pendulum A is lifted to a displacement A at t = 0 and

released from rest while B remains at its equilibrium position at t = 0. The constants can be

solved (see Exercise 4) to give the subsequent motions of the pendulums to be

+

−= t

2

ωωcost

2

ωωcosA(t)x 1212

A

+

−= t

2

ωωsint

2

ωωsinA(t)x 1212

B (12)

The motions of the pendulums A and B exhibit a typical beat phenomenon. The motion can be

understood as oscillations with a time period ( )12/4 + and a sinusoidally varying amplitude

)t2

cos(A)t(A 12 −= with the amplitude becoming zero with a period of ( )12/2 − . As

an example, Figure 3(a), 3(b) show plots of x(t) = sin(2t)sin(50t) and x(t)=cos(2t)cos(50t)

vs. t respectively.

Fig. 3(a) Fig. 3(b)

PROCEDURE:

1. Uncouple the pendulums. Set small oscillations of both pendulums individually. Note

the time for 20 oscillations and hence obtain the average time period for free

oscillations of the pendulums and the natural frequency 0.

2. Couple the pendulums by hooking the spring at some position to the vertical rods of the

pendulums. Ensure that the spring is horizontal and is neither extended nor hanging

loose to begin with.

3. Excite the first normal mode by displacing both pendulums by the same amount in the

same direction. Release both pendulums from rest. Note down the time for 20

oscillations and hence infer the time period T1 and frequency 1 of the first normal

mode.

4. With the spring at the same position excite the second normal mode of oscillation by

displacing both pendulums in the opposite directions by the same amount and then

releasing them from rest.Note down the time for 20 oscillations and hence infer the time

period T2 and frequency 2.

5. Repeat these measurements for the spring hooked at 3 more positions on the vertical

rods of the pendulums..

(Note: Your measurements will be more accurate only if you choose somewhat smaller

than the total length L, i.e. choose a position of the coupling spring which is intermediate

in position).

OBSERVATIONS:

1) Mass of the bob (𝑚𝑏) =

Mass of the rod (𝑚𝑟) =

Length of the rod (𝐿𝑟) =

Length of the bob (𝐿𝑏) =

2) Mass of each pendulum (m) = 𝑚𝑏+ 𝑚𝑟

Length of each pendulum (L) =𝑚𝑟.(

𝐿𝑟2

) + 𝑚𝑏.( 𝐿𝑏)

𝑚𝑏+ 𝑚𝑟

3) Moment of Inertia of pendulum = m𝐿2

TABULAR COLUMN :

For Uncoupled Oscillator :

Length of the string = -----------------------------cm.

Time taken for 20 uncoupled oscillations

of

Average

T=𝐴+𝐵

2

sec

Time Period

T0 = T/20

Angular

frequency

0=2/T0(sec−1) Pendulum A Pendulum B

For Coupled Oscillator:

S.No Position

of

spring

from

pivot

(cm)

Mode 1(Parallel) Mode 2 (Anti parallel)

Time for 20

oscillations

T(sec)

Time

Period

T1= 𝑇

20

(sec)

Angular

frequency

1(sec-1)

Time for 20

oscillations

T(sec)

Time

Period

T2=𝑇

20

(sec)

Angular

frequency

2 (sec-1)

1 10

2 15

3 20

4 25

Model Graph:

Calculations:

On the same graph paper plot 12/0

2 (OR) 22/0

2 vs 2 .

Obtain the slope of the graph of 22/0

2 vs 2 and hence obtain the spring constant” k “of the

coupling spring.

Slope = 2k / (mgL) = ______________________

Spring constant (k) = 𝑆𝑙𝑜𝑝𝑒∗𝑚𝑔𝑙

2= ________________dynes/cm

RESULT: The spring constant of a given coupled oscillator (K): ______________ dynes/cm

SPACE FOR THE GRAPH

7. LCR - CIRCUIT

AIM: To determine the resonant frequency and quality factor of LCR circuit in series and

parallel.

APPARATUS: Capacitor, resistor, voltmeter, ammeter, frequency, generator, inductor,

connecting wires

PRINCIPLE: If the value of the frequency of applied signal is so adjusted that the impedance of

the circuit becomes minimum. The current flowing through the circuit will be maximum. This

particular frequency at which the impedance of the circuit becomes minimum and therefore the

current becomes maximum is called the resonant frequency.

FORMULA: Quality factor 𝑄 =𝑓

𝑟

|𝑓 1−𝑓

2|

Resonant frequency for LCR circuit in series and parallel connections

Where, 𝑓 𝑟 =

1

2𝜋√𝐿𝐶

𝑓 𝑟 = Resonant frequency in Hz

L = Inductance in henrys

C = capacitance in faradays

THEORY: We know that inductive reactance XL = 2πfL means inductive reactance is directly

proportional to frequency (XL and prop ƒ). When the frequency is zero or in case of DC,

inductive reactance is also zero, the circuit acts as a short circuit; but when frequency increases;

inductive reactance also increases. At infinite frequency, inductive reactance becomes infinity

and circuit behaves as open circuit. It means that, when frequency increases inductive reactance

also increases and when frequency decreases, inductive reactance also decreases. It is clear from

the formula of capacitive reactance XC = 1 / 2πfC that, frequency and capacitive reactance are

inversely proportional to each other. In case of DC or when frequency is zero, capacitive

reactance becomes infinity and circuit behaves as open circuit and when frequency increases and

becomes infinite, capacitive reactance decreases and becomes zero at infinite frequency, at that

point the circuit acts as short circuit.

The inductive and capacitive reactance becomes equal and the frequency, at which these two

reactance become equal, is called resonant frequency, fr. At resonant frequency, XL = XC

At resonance f = fr and on solving above equations we get ,

𝑓 𝑟 =

1

2𝜋√𝐿𝐶

PROCEDURE:

1. Connect the circuit as shown in figure. Connect resistance R, capacitor C and inductor L in

the circuit in series and parallel.

2. Connect function generator across input of the circuit as shown in figure.

3. Switch ON the function generator using ON/OFF switch provided on the front panel. Set the

output of function generator to sine wave signal of approximately 3VAC RMS and set the

frequency at 100Hz.

4. Increase the frequency in small steps towards 10 KHz and every time note down the

observations in the table no.1 & 2 . At a particular frequency, we can observe the maximum

current in the series LCR circuit and Minimum current in the LCR parallel circuit , that particular

frequency is called Resonant frequency.

5. Repeat the procedure for different values of L,R and C.

6. Plot a graph between frequency Vs current by taking frequency on X-axis and current on Y-

axis as shown in the model graphs.

7. From the graph calculate the band width for series and parallel circuits.

8. Then find the Quality factor (Q) for both series and parallel connections.

Circuit for LCR Series: model graph:

Fig 1

SERIES LCR CIRCUIT :

S.No Frequency (Hz) Current (mA)

L = --------------------- mH

C = --------------------- µF.

R= ---------------------- Ω

CALCULATIONS:- Calculation from the graph(series resonant circuit)

1. Band width ∆𝑓 = |𝑓 1−𝑓

2|

2. Quality factor 𝑄 =𝑓

𝑟

|𝑓 1−𝑓

2|

3. Resonant frequency 𝑓 𝑟 =

1

2𝜋√𝐿𝐶

CIRCUIT FOR LCR PARALLEL:

Parallel LCR Circuit

. L = --------------------- mH

C = --------------------- µF.

R= ---------------------- Ω

S.No Frequency (Hz) Current (mA)

Calculation from the graph (parallel resonant circuit)

1. Resonant frequency ( 𝒇𝒓)=

2. Band width ∆𝑓 = |𝑓1−𝑓2|

3. Quality factor 𝑄 =𝑓𝑟

|𝑓1−𝑓2|

Result: Resonant frequency for LCR Series Circuit ( 𝒇𝒓) = ________ Hz

Resonant frequency for LCR Parallel Circuit (𝒇𝒓) = ________ Hz

Quality factor for LCR Series Circuit (Q) =___________

Quality factor for LCR Parallel Circuit (Q) = ___________

VIVA VOCE

1. What is the function of A.F. oscillator?

An A.F oscillator is a device which can produce sinusoidal waveforms of any desired

frequency ranging from 20Hz to 20 KHz.

2. What do you mean by sharpness of resonance?

It is a measure of the rate of fall of current amplitude from its maximum value at

resonance frequency to on either side of it.

3. What is resonance frequency?

The frequency at which the resonance occurs is called resonance frequency.

4. What is meant by resonance?

When the applied frequency matches with the natural frequency of a body, the amplitude

of vibration becomes maximum. This phenomenon is called resonance.

5. What is bandwidth of series circuit?

The range of frequencies between the cut-off frequencies is called bandwidth.

6. Define quality factor of a series circuit.

The ratio of a resonant frequency of a circuit to its bandwidth is called quality factor.

7. Why is the series circuit called as acceptor circuit?

Because it accept one frequency component out of the input signals having different

frequencies. The accepted frequency is equal to its own resonance frequency.

8. Why parallel resonance circuit is called a rejecter circuit?

Because it rejects the signal having same frequency as its own frequency.

9. What is the importance of series resonance circuits?

For high frequency A.C in radio communications, a series resonance circuit is used. LCR

circuits are used in frequency filter circuits like high pass filter, low pass filter and band

pass filter.

SPACE FOR GRAPH SHEET

SPACE FOR GRAPH SHEET

8 .LASER DIODE CHARACTERISTICS

AIM: To study the V-I and P-I characteristics of LASER sources.

APPARATUS: Micro Laser Diode Characteristics board comprising of:

1. Laser diode.

2. 0-5 V variable supply for laser diode.

3. 20 mW digital optical power meter to measure optical power of Laser diode.

4. 20 V digital voltmeter to measure voltage across laser diode.

5. 200 mA dc digital ammeter to measure laser diode current.

THEORY: Laser diodes are electronic devices which work on the principle of

electroluminescence.

These are made up of direct band gap materials (materials for which maximum of valence

band and minimum of conduction band lie for same value of K) Example: GaAs, InP etc

Materials for which maximum of valence band and minimum of conduction band do not

occur at same value of K are called indirect band gap materials. Example: Si and Ge

CIRCUIT DIAGRAM:

+

R mA

Laser Source V Photo

Detecto

r

W

Electrical Characteristics:

The V-I curve: The voltage drop across the laser is often acquired during electrical

characterization. This characteristic is similar to the analogous characteristic of any other type of

semiconductor diode and is largely invariant with temperature, as depicted in Figure 1.The

typical voltage drop across a diode laser at operating power is 1.5 volts. V-I data are most

commonly used in derivative characterization techniques.

PROCEDURE FOR V-I CHARACTERISTICS OF A LASER DIODE:

1. Connect the circuit as per the circuit given.

2. Slowly increase supply voltage using variable power supply using coarse and fine knobs.

3. Note down the current through the laser diode at increasing values of laser diode voltage

of 0.5 V, 1.0 V, 1.5 V, 2.5 V.

4. Do not exceed current limit of 30 mA else the laser diode may get damaged.

5. Plot a graph of laser diode voltage Vs laser diode current as shown in figure 1. (As this

experiment is conducted at room temperature, only one graph for a single temperature

will be obtained).

OBSERVATIONS:

S.No. Voltage (V) Current (mA)

Graph:

The P-I Curve.

The most common of the diode laser characteristics is the P-I curve. It plots the drive

current applied to the laser against the output light intensity. This curve is used to

determine the laser’s operating point (drive current at the rated optical power) and

threshold current (current at which lasing begins). The efficiency of a diode laser is also

derived from the P-I curve. It is most commonly expressed as slope efficiency and

measured in units of mW/mA.

We know that,

Power (P) α I2R

Where, I is current and

R is resistance.

As, voltage increases current increases (V α I) and as current increases the intensity of

laser diode increases and as a result the number of electrons which are coming out of the

laser diode increases. Hence the reading of wattmeter will also increase.

PROCEDURE FOR P-I CHARACTERISTICS OF LASER DIODE:

1. Connect the laser diode circuit as shown below.

2. Slowly increase supply voltage (current) using variable power supply coarse and fine

knobs.

3. Note down the optical power measured by the optical power meter in mW at

increasing current through the laser diode from 5 mA to 26 mA at 1 mA step.

4. Do not exceed current limit of 30 mA else the laser diode may get damaged.

5. Plot a graph of laser diode optical power Vs laser diode current as shown in figure 2.

(As this experiment is conducted at room temperature, only graph for a single

temperature will be obtained.)

OBSERVATIONS:

S.No Current(mA) Power(mW)

GRAPH:

RESULT: ______ and ______ characteristics of laser diode are studied.

VIVA VOCE:

1. What are n-type and p-type semiconductors?

An n-type semiconductor is created by adding pentavalent impurities like phosphorus (P),

arsenic (As), or antimony (Sb). A pentavalent impurity is called a donor because it is

ready to give a free electron to a semiconductor.

p-type Semiconductor is created due to addition of trivalent impurities such as boron,

aluminum or gallium to an intrinsic semiconductor creates deficiencies of valence

electrons called "holes".

2. Explain the working of a laser diode?

Forward biasing to cause population inversion and hence stimulated emission.

3. What do you understand from V-I characteristics of a laser diode?

After Knee voltage, as the voltage increases the current increases i.e; V α I

4. What do you understand from P-I characteristics of a laser diode?

As, voltage increases current increases (V α I) and as current increases the intensity of

laser diode increases as a result the number of electrons which are coming out of the laser

diode increases. Hence the reading of wattmeter will also increases. i.e; V α L.

5. What type of biasing is used in this experiment?

Forward biasing to cause population inversion and hence stimulated emission.

6. What are the real time applications of laser diode?

CD and DVD players,

Barcode scanners,

Remote control applications

Fiber optic communication

Integrated circuits

Long distance communications.

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9. DETERMINATION OF NUMERICAL APERTURE AND BENDING LOSSES IN

OPTICAL FIBRE

AIM: To determine the Numerical aperture and bending losses of Optical fibers.

APPARATUS: An optical fiber cable, optical fiber trainer board, screen, NA jigs, Mandrel,

patch cards.

FORMULA:

𝐍𝐀 =𝐖

√(𝟒𝐋𝟐 + 𝐖𝟐)= 𝐒𝐢𝐧𝛉𝐚

Where W = Diameter of the light falling spot on the screen

L = Distance between the optical fiber end and the screen

𝜃𝑎 = Acceptance angle

Attenuation is defined as the ratio of the optical input power to the output power in the fiber

of length L.

∝= −𝟏𝟎

𝑳𝒍𝒐𝒈 (

𝑷𝒊𝒏

𝑷𝒐𝒖𝒕) 𝒅𝑩/𝒌𝒎

Where, Pin = Input Power (Transmitted)

Pout =Output Power (Received)

α is Attenuation constant

L is length of optical fiber = 1 meter cable

Therefore LOSS = Pin-Pout dB/m

A decibel (dB) is a unit used to express relative differences in signal strength.

A decibel is expressed as the base 10 logarithm of the ratio of the power of two signals

(Pin and Pout).

dB = 10 × 𝐿𝑜𝑔10(P1/P2)

Where 𝐿𝑜𝑔10 is the base 10 logarithm, and P1 and P2 is are the powers to be compared.

THEORY:

Numerical aperture of an optical fiber is defined as the light gathering ability of the optical fiber.

It also refers to the maximum angle at which the light incident on the fiber end is totally

internally reflected and is properly transmitted along the fiber.

Acceptance angle (θ0) is the maximum angle made by the light ray with the fiber axis, so that

light can propagate through the fiber after total internal reflection.

Acceptance cone is derived by rotating the acceptance angle about the fiber axis.

Fig: Experimental setup

Light from the optical fiber end at A falls on the screen is BC. Let the diameter of the light

falling spot on the screen is W=BC

Let the distance between the optical fiber end and the screen is L=BC=W

BC = DC = 𝑊

2 from Geometry

𝐴𝐵 = [𝐿2 +𝑊2

4]

1

2 =>𝐴𝐵 =(4𝐿2+𝑊2)

12

2

𝑁𝐴 =𝑊

(4𝐿2+𝑊2)1/2= 𝑆𝑖𝑛𝜃𝑎------------------(1)

Where θa is acceptance angle. By knowing the values of W and L you can compute the

numerical aperture and h

Procedure for Numerical Aperture:

1. Connect one end of the optical fiber cable to transmitter of the optical fiber trainer board and

the other end to the numerical aperture jig.

2. Hold the white screen which consists of no. of concentric circles (5, 10,15,20,25 mm

diameter) vertically at suitable distance to make the red spot emitted from the optical fiber

coincide with the 5 mm circle which is W. Note that the circumference of the spot

(outermost) must coincide with the circle.

3. Note L, i.e., the distance between optical fiber end and the screen .

4. Compute the Numerical Aperture (NA) of the optical fiber by using the formula.

NA = Sinθa = 𝑊

(4𝐿2+𝑊2)1/2

5. Where θa is the Acceptance angle

6. Tabulate the readings and repeat the experiment for 10 mm,15 mm , 20mm and 25mm

diameter too.

7. Take the average of all NA readings.

Procedure for Bending Losses:

1. Connect one end of optical fiber to the reference light source and the second end to

the optical power meter. Make sure that the optical fiber is straight and no bends or

loops are present.

2. Connect the optical power meter terminals to power display unit through patch cards

(Red to Red, Black to Black terminals).

3. By using the variable knob select certain amount of power to be transmitted through

the optical fiber.

4. Hold the optical fiber straight and note the power reading displayed in the power

meter as Pin.

5. Bend the optical fiber for one turn with the help of mandrel and note the power meter

reading.

6. Repeat the same procedure for four turns and note the readings.

7. Take the mean of all these readings as Pout.

8. The difference of Pin and Pout is the loss of power due to bending of optical fiber.

9. Take the average of all the readings and divided by 10 to measure the bending loss of

given optical fiber.

TABULAR FORM:

S.No

Distance between

the optical fiber

end and the screen

L (mm)

Diameter of the

light spot

falling on the

screen W(mm)

Numerical

Aperture (NA)

Acceptance Angle

θ (degrees)

CALUCULATIONS:

To Determine bending losses in optical fiber:

S.No Output power

Without

bending of

Optical

Fiber(Pin)

Out power with bending of Optical Fiber(Pout)dB Loss=

Pin-Pout

(dB)

1 turn 2 turn 3turn 4turn Mean

CALCULATION:

Result: The numerical aperture of the given optical fiber cable is____________ and the bending

losses in the given optical fibre is _____________dB/Km

VIVA VOCE

1. What are various parts of optical fiber?

Core - Thin glass center of fiber where light travels

Cladding - Outer optical material surrounding the core

Buffer jacket - Coating that protects the fiber.

2. How should be the refractive index of core and cladding?

Refractive index of core should be high compared to cladding for TIR.

3. What is the basic principle behind the propagation of light through optical fiber?

Total Internal Reflection.

4. What is Total Internal Reflection?

When the light rays launched from denser medium at an angle of incidence greater than

the critical angle, then all the light rays are reflected back into the denser medium.

5. What is critical angle?

The incidence angle in denser medium for which the angle of refraction is 90° in rarer

medium.

6. Define Attenuation in optical fiber?

Attenuation in an optical fiber is caused by absorption, scattering, and bending

losses. Attenuation is the loss of optical power as light travels along the fiber. Signal

attenuation is defined as the ratio of optical input power (Pi) to the optical output power

(Po).

7. Define Numerical aperture?

The sin of acceptance angle is called as Numerical Aperture.

8. What is the significance of Numerical aperture?

It gives the Light gathering ability of an optical fiber.

9. What is Acceptance angle?

Acceptance angle (θa) is the maximum angle made by the light ray with the fiber axis,

so that light can propagate through the fiber after total internal reflection.

10. What is Acceptance cone?

Acceptance cone is derived by rotating the acceptance angle about the fiber axis.

11. What are various attenuations present in optical fiber?

The various losses in optical fiber cable are due to

Absorption

Scattering

Bending

Dispersion

12. Losses in optical fibers are measured in ___________unit?

dB/kilometer

10. ENERGY GAP OF A SEMI-CONDUCTOR

AIM: To determine the energy gap of a semiconductor diode.

APPARATUS: Micro Board Kit consists of Germanium semiconductor diode, micro ammeter,

regulated dc power supply, thermometer, oven, copper vessel, Bakelite lid and connecting wires.

FORMULA: Energy gap Eg = 2 x slope x Boltzmann constant (K) x 2.303 eV

1.6 x 10−19

Here Boltzmann constant K =1.38×10-23 J/K

THEORY:

In a semiconductor there is an energy gap between its conduction and valance band. For

conduction process certain amount of energy is to be given and the energy needed is the measure

of energy gap, Eg of the semiconductor. When a P-N junction diode is reverse biased, current is

due to minority carriers whose concentration is dependent on Eg. The reverse current Is is a

function of temperature of the junction diode.

The energy band gap of different semiconductor like Si, Ge, Gap, GaAs etc are different, hence

by determining the energy gap we can identify the type of semiconductor used to prepare the

diode .

Energy Band Diagram:

CIRCUITDIAGRAM:

PROCEDURE:

1. Connect all the connections as per the circuit diagram.

2. Kit and heater are to be turned off while making the connections.

3. After making the connections switch on the kit.

4. Now fix the voltage at 1.5 V.

5. Insert the thermometer in to the slot provided and switch on the heater.

6. Now allow the temperature to rise up to 60 0C, and then switch off the heater.

7. Wait until the temperature is raised to 70 0C or 80 0C and becomes stable.

8. After some time, the temperature will begin to fall.

9. Note down the current value (in μA) using ammeter for every 5 0C fall of temperature.

10. This value of current will be known as saturation current Is for that specific temperature.

11. Note down the readings until the temperature reaches 30 0C.

12. Note down all the observations in the tabular form given below.

OBSERVATIONS:

S.No Current( Is )

in μA

Temperature(t) in 0C

Temperature(T)

in Kelvin(t+273)

1/T Log10Is

1

2

3

4

5

6

7

8

9

10

GRAPH:

A graph is drawn between Log10Is and 1/T. It is a straight line for which slope is measured.

CALCULATIONS:

Energy gap Eg = 2 x slope x Boltzmann constant (K) x 2.303 eV

1.6 x 10−19

Here Boltzmann constant K = 1.38 x 10-23 J/K.

Slope(m) = 𝑦2−𝑦1

𝑥2−𝑥1

RESULT:

The energy gap of germanium semiconductor diode is______________eV

VIVA VOCE

1. What is a semiconductor?

A semiconductor is a material which has energy gap between that of conductor such a

copper and insulator such as glass.

2. What is Forward and reverse biasing?

Forward bias: When the positive terminal of the battery is connected to the p-type

material and the negative terminal of the battery is connected to the n-type material.

Reverse bias: When the positive terminal of the battery is connected to n-type material

and the negative terminal of the battery is connected to the p-type material.

3. What is energy gap?

The gap between the valance band and conduction band on energy level diagram.

4. What is intrinsic and extrinsic semiconductor?

Intrinsic semi conductor: A pure semiconductor is known as intrinsic semiconductor.

Extrinsic semi conductor: A pure semiconductor after doping is called extrinsic or impure

semiconductor. Trivalent and pentavalent impurities are added to form p type and n type

extrinsic semiconductors respectively.

5. Define P-type and N-type semiconductors respectively.

N-type: It is a extrinsic semiconductor which is obtained by doping the pentavalent

impurity like As, Sb, Bi to pure semiconductor. P-type:It is a extrinsic semiconductor

which is obtained by doping the trivalent impurity like Ga, I, B to pure semiconductor.

6. What is doping?

The process of adding impurities to a pure semiconductor is called doping, the material

added as impurity is called as dopant.

7. Why are readings taken only while cooling?

Because heating is non-linear where as cooling is linear and it follows Newton’s law of

cooling.

8. Why is the diode reverse biased in this experiment?

Reverse bias diode equation 𝐼𝑑 = Is[exp ( ev

kT ) − 1 Reverse saturation current Is

dependent on temperature T, hence we choose reverse bias to determine energy gap.

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