xperiment -1engineeringphysics.weebly.com/uploads/8/2/4/3/... · Wave length of sodium light = 5893...
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Transcript of xperiment -1engineeringphysics.weebly.com/uploads/8/2/4/3/... · Wave length of sodium light = 5893...
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xperiment -1
STEWART AND GEE’S METHOD
Aim:- Tostudythevariationofmagneticfieldalongtheaxis ofacircularcoilcarryingcurrent.
Apparatus:-Stewart&Gee’s galvanometer, battery,key,rheostat,
ammeterandconnectingwires.
Formula:- The magnetic field at any point along the axis of the coil is
𝐵 =𝜇0𝑛𝑖𝑎
2
2 𝑋2 + 𝑎2 3 2 (𝑇𝑒𝑠𝑙𝑎)
Where 𝜇0 = permeability of free space
𝑛 = Number of turns in the coil
𝑖 = Current passing through the coil
𝑎 = Radius of the coil
𝑋 = Distance from the coil
Description:Theapparatusconsistsofacircularframemadeupofnon-magneticsubstance.
Insulatedwiresareconnectedtotheterminalsandtwotapingfromthecoilareconnectedtothe
othertwoterminals.Byselectingapair ofterminals thenumberofturns usedcanbechanged.The
frameisfixedtoalongbaseBatthemiddleinaverticalplanealongthebreadthside.Thebase
haslevelingscrews.Arectangularnon-magneticmetalframeissupportedontheuprights.The
planeoftheframecontains theaxisofthecoilandtheseframeposses throughthecircularcoil.A
magneticcompasslikethat oneused indeflectionmagnetometer issupportedonamovable
platform.Thisplatformcanbemovedontheframealongtheaxisofthecoil.Thecompassisso
arrangedthatthecenterofthemagneticneedlealwayslies ontheaxis ofthecoil.
Theapparatusisarrangedsothattheplaneofthecoilisonthemagneticmeridian.The
framewithcompassiskeptatthecenterofthecoilandthebaseisrotatedsothattheplaneofthe
coilis paralleltothemagneticneedleinthecompass.Thecompassis
rotatedsothatthealuminum pointerread00-00.Nowthe rectangularframeis along East-
Westdirections.
Theory:Whenacurrentofi-amperesflows throughacircularcoilofn-turns,eachofradius‘a’,
themagneticinductionatanypoint‘p’ontheaxisofthecoilis givenby
𝐵 =𝜇0𝑛𝑖𝑎
2
2 𝑥2 + 𝑎2 3/2… (1)
Where ‘𝑥’is thedistanceofthepoint‘𝑝’fromthecentreofthecoil.
4
Observations
Current flowing through the coil i = 0.5A
Number of turns o the coil n = 50
Radius of the coil a = 10.35 cm = 0.1035 m
Horizontal component of the earth’s field Be = 0.38x10-4
To determine the magnetic field along the axis of the circular coil carrying current
Distance
X (cms)
Deflection in East side
ETan
Deflection in West side
WTan
2tan WE
eBB
𝐵
=𝜇0𝑛𝑖𝑎
2
2 𝑋2 + 𝑎2 3 2
One
direction
Opposite
direction EAvg
One direction Opposite direction WAvg
1 2
3 4 5 6
7 8
0
5
10
15
63
30
15
10
64
31
17
10
55
35
18
10
55
35
18
9
59.5
32.5
15
9.75
1.6976
0.6370
0.2679
0.1718
33
25
14
9
35
26
15
10
55
43
23
10
54
43
23
9
44.5
34.2
18.7
9.5
0.9826
0.6796
0.3384
0.1673
4.77x10-5
2.35x10-5
1.062x10-5
0.594x10-5
3.99x10-5
2.314x10-5
1.066x10-5
0.942x10-5
5
Whenthecoilisplacedinthemagneticmeridian,thedirectionofthemagneticfieldwill
beperpendicular tothemagneticmeridian;i.e.,perpendiculartothedirectionofthehorizontal
componentoftheearth’sfield;sayBe.Whenthedeflectionmagnetometerisplacedatanypoint
ontheaxisofthecoilsuchthatthecentreofthemagneticneedleliesexactlyontheaxisofthe coil,
thentheneedleis acteduponbytwofieldsBandBe,whichareatrightangles tooneanother.
Therefore, theneedledeflectsobeyingthetangentlaw,
𝑩 = 𝑩𝒆 𝐭𝐚𝐧∅𝒆 + ∅𝒘
𝟐… (𝟐)
Be, the horizontalcomponent of the earth’s field is taken fromstandard tables. The
intensityofthefieldatanypointis calculatedfromequation(2)andverifiedusingequation(1).
Procedure:Themagnetometeriskeptatthecenterofthecoilandrotatedsothatthealuminum
pointerreads 00 − 00 . Twoterminalsofthecoilhavingpropernumberofturnsareselectedand
connectedtothetwoopposite terminalsofthecommutators.Abattery,key,ammeteranda
rheostatisadjustedsothatthedeflectionisabout 600 .Theammeterreading‘i’isnoted.Thetwo
endsofthealuminumpointerareread(θ1,θ2).Thenthecurrentthroughthecoilreversedusing
commutatorsandthetwoendsof aluminumpointerareread(θ3,θ4).Theaveragedeflectionsθis
calculated.Themagnetometerismovedtowards eastinsteps
of2cmeachtimeandthedeflections
beforeandafterreversalofcurrentarenoted,untildeflectionsfallsto 300 .Theexperimentis
repeatedbyshiftingthemagnetometertowardswestfromthecentreofthecoilinstepsof2cm,eac
htimeanddeflections arenotedbeforeandafterreversalofcurrent.
Precautions:-
1. Galvanometershouldnotbedisturbedwhilemakingprimaryadjustments.
2.Ferromagneticmaterialsmustbekeptaway.
Results:-Thevariationofmagneticfieldalong the axis of a circular coil withthedistanceis studied.
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Experiment -2
Newton’s Rings
Aim:To observe Newton rings formed by the interface of produced by a thin air film and
todetermine the radius of curvature of a Plano-convex lens.
Apparatus:Traveling microscope, sodium vapour lamp, plano-convex lens, plane glass plate,
magnifyinglens.
Formula:-
The radius of curvature (R) of the given Plano-convex lens is obtained from the relation
4
SlopeR
R= radius of curvature of plano convex lens.
Wave length of sodium light 𝜆 = 5893𝐴0 = 5893 × 10−8𝑐𝑚
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.
Basic Theory:
When a plano-convex lens (L) of long focal length is placed on a plane glass plate (G) , a thin
film of air is enclosed between the lower surface of the lens and upper surface of the glass plate.
The thickness of the air film is very small at the point of contact and gradually increases from the
center outwards. The fringes produced are concentric circles. With monochromatic light, bright
and dark circular fringes are produced in the air film. When viewed with the white light, the
fringes are coloured.
A horizontal beam of light falls on the glass plate B at an angle of 450. The plate B reflects a part
of incident light towards the air film enclosed by the lens L and plate G. The reflected beam from
the air film is viewed with a microscope. Interference takes place and dark and bright circular
fringes are produced. This is due to the interference between the light reflected at the lower
surface
of the lens and the upper surface of the plate G.
For the normal incidence the optical path difference Between\ the two waves is nearly2µt,
where µ is the refractive index of the film and t is the thickness of the air film.
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Model graph Interference fringe pattern:
D2cm2
n n +2 n +2 n Number of the ring (n)
9
Here an extra phase difference π occurs for the ray which got reflected from uppersurface of the
plate G because the incident beam in this reflection goes from a rarermedium to a denser medium.
Thus the conditions for constructive and destructiveinterference are (using µ = 1 for air)
2 t = nfor minima; n =0,1,2,3… … … … (1)
and 1
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t n
for maxima; ; m = 0,1,2,3… … …(2)
Then the air film enclosed between the spherical surface
of R and a plane surface glass plate, gives circular rings
such that
rn2 = (2R-t)t
where rn is the radius of the nth
order dark ring .
(Note: The dark ring is the nth
darkring excluding the central dark spot).Now R is the order of 100
cm and t is at most 1 cm. Therefore R>>t. Hence (neglecting the t2
term ), giving
2
2 nrtR
Putting the value of “ 2 t” in eq(1) gives
2
2 nr
R
With the help of a traveling microscope we can measure the diameter of the nth
ringorder dark
ring = Dn Then 2
mn
Dr and hence,
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4
nDR
n
The value of
2
nD
nis calculated from the slope of the graph drawn in between n Vs
2
nD
4
SlopeR
So if we know the wavelength , we can calculate R(radius of curvature of the lens).
II. Setup and Procedure:
1. Clean the plate G and lens L thoroughly and put the lens over the plate with thecurved
surface below B making angle with G
2. Switch in the monochromatic light source. This sends a parallel beam of light.This beam
of light gets reflected by plate B falls on lens L.
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Ob
se
rvation
s:
Slo
pe
(fr
om
n -
D2 g
rap
h)
valu
e
=0
.02
72
The
rad
ius o
f cu
rvatu
re (
R)
=
11
5.3
9 c
m
cm
To D
ete
rmin
e th
e
dia
me
ter
of a
Pla
no
co
nve
x le
ns b
y fo
rmin
g
New
ton
’s r
ing
s
D2
(cm
2)
0.0
71
2
0.0
94
8
0.1
76
4
0.2
19
9
0.2
89
4
Dia
me
ter
(D)
(cm
)
„a~
b‟
0.2
67
0.3
08
0
.42
0
.46
9
0.5
38
Tra
ve
llin
g M
icro
sc
op
e R
ea
din
gs
Rig
ht
To
tal
PS
R+
(HS
R×
LC
)
„a‟
(c
m)
11
.76
1
11
.72
6
11
.69
1
11
.65
9
11
.62
7
HSR
61
26
91
59
27
PS
R
(cm
)
11
.7
11
.7
11
.6
11
.6
11
.6
Left
To
tal
PS
R+
(HS
R×
LC
)
„a‟
(c
m)
12
.02
8
12
.06
9
12
.11
1
12
.12
8
12
.16
5
HSR
28
69
11
28
65
PS
R (
cm
)
12
12
. 1
2.1
1
2.1
1
2.1
5
No
.of
rin
g
n
2
4
6
8
10
11
Look down vertically from above the lens and see whether the center is wellilluminated. On
looking through the microscope, a spot with rings around it canbe seen on properly focusing the
microscope.
3. Once good rings are in focus, rotate the eyepiecesuch 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 passesthrough the center of the ring system.
4. Now move the microscope to focus on a ring (say, the 20th order dark ring). Onone side of
the center. Set the crosswire tangential to one ring.Note down the microscope reading .
5. Move the microscope to make the crosswire tangential to the next ring nearer tothe center
and note the reading. Continue with this purpose till you pass throughthe center. Take
readings for an equal number of rings on the both sides of thecenter.
Calculations:
Plot the graph of D2Vs n and draw the straight line of best fit.
Give the calculation of the best fit analysis below. Attach extra sheets if necessary.
From the slope of the graph, calculate the radius of curvature R of the plano convex lensas
R= Dn2-Dm
2 /4(n-m)λ____________________________ cm.
Precautions:
Notice that as you go away from the central dark spot the fringe width decreases. In order to
minimize the errors in measurement of the diameter of the rings the following precautions should
be taken:
i) The microscope should be parallel to the edge of the glass plate.
ii) If you place the cross wire tangential to the outer side of a perpendicular ring on one
side of the central spot then the cross wire should be placed tangential to the inner side of
the same ring on the other side of the central spot.
iii) The traveling microscope should move only in one direction.
Results:Radius of Curvature of a given Plano Convex lens ( R )=…115.39 cm
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Experimental arrangement
l
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Experiment- 3
Air wedge: Interference of light
Aim:To measure the diameter of a given thin wire using interference patterns formed using and
extended source, at the air wedge between two glass plates.
Apparatus:
Glass plate, thin wire, beam splitter, light source, traveling microscope etc.
Formula:-
The diameter (d) of the given thin wire
𝑑 =𝜆𝑙
2𝛽 (𝑐𝑚)
Where λ = wavelength of the light used.
l = Distance between the point of the two glass plates and the axis of wire fixed between them
= Fringe width
Theory:
Interference effects are observed in a region of space where two or more coherent waves are
superimposed. Depending on the phase difference, the effect of superposition is to produce
variation in intensities which vary from a maximum of (a1+ a2)2 to a minimum of (a1– a2)
2 where
a1and a2are amplitude of individual waves. For the interference effects to be observed, the two
waves should be coherent. Interference patterns can be observed due to reflected waves from the
top and bottom surfaces of a thin film medium. Because of the extended source, the fringes are
localized at or near the wedge.
shows the cross sectional view of the two flat glass plates kept on each other and separated by a
wire at therightmost end. There is a thin air film between the two glass plates due to the wire kept
at the right end.The path difference between the two rays r1 and r2 is 2t cosr , where „t‟ is the air
thickness.
The condition for dark band is,
2tCosr = m
If the incident ray is close to normal ,
2t = m………………(1)
For m=N, the maximum order of the dark band the path difference will be maximum and
thiscorrespond to the position where the wire is kept . Moreover, here the fringes are equal
thickness fringes. So eqn (1) can be written as
14
To determine the fringe width of parallel fringes
S. No Fringe
number
Travelling Microscope reading Width of ____fringes
(cm) PS.R
“a” (cm) H.S.R
H.S.R×L.C “b” (cm)
Total “(a+b)”(cm)
1
2
3
4
5
6
7
8
9
10
11
n
n+2
n+4
n+6
n+8
n+10
n+12
n+14
n+16
n+18
n+20
8.2 8.2 8.2 8.1 8.1 8.1 8 8 8 7.9 7.9
98
59
23
88
50
21
87
48
21
95
63
0.098
0.059
0.023
0.088
0.050
0.021
0.087
0.048
0.021
0.095
0.063
8.298
8.259
8.223
8.188
8.150
8.121
8.087
8.048
8.021
7.095
7.963
0.039
0.036
0.035
0.038
0.029
0.034
0.039
0.027
0.026
0.032
Total ‘x’=--------0.335---- cm
Average width of the two fringes (y) =𝑥
10= 0.0335 : cm
Fringe width β = 𝑦
2= 0.01675 : cm
Wave length of the light used λ : 5963 A0
: cm
Distance between the point of the two glass plates and
the axis of wire fixed between them l :4.8 cm
The diameter (d) of the given thin wire 𝑑 =𝜆𝑙
2𝛽 : 8.44x10-3 cm
:
15
2d = N………………………. (2)
The length „L‟ can be written as
L = N …………………. (3)
where is the fringe width. From eq (2) and (3),
d=L/2 --------------------------(4)
Procedure:
Place the two optically flat glass plates one over the other , so that they touch each other at
the left end and are separated at the right end by the given thin wire . The length of the
wire should be perpendicular to the length of the glass plate.
Place this assembly on the platform of the microscope such that the length of the glass
plate is parallel to the horizontal traverse of the microscope.
Illuminate the assembly by sodium light. Adjust the glass plate G, such that incident light is
almost normal to the glass plate wire assembly.
Focus the microscope to observe the interference patterns
Measure the horizontal positions of the dark bands in the order of say, n, n+2, n+4, ---- by
traversing the microscope horizontally.
Determine the length „L‟ with the help of microscope.
Plot a graph of horizontal positions versus order of dark band. Find out the mean fringe
width b from the graph and calculate
the thicknessof the given wire.
Results:
The determined diameter of a thin wire using parallel fringes by interference method is ___:
8.44x10-3_cm
16
Circuit Diagram:
17
Experiment-4
ENERGY GAP OF A SEMICONDUCTOR DIODE
Aim:Todeterminetheenergygapofasemiconductordiode.
Apparatus:Germanium diode(0A79), thermometer, copper vessel, regulated DCpower
supply,microammeter, heaterandBakelitelid.
Formula:-
𝑒𝑛𝑒𝑟𝑔𝑦 𝑔𝑎𝑝𝐸𝑔 =2.303 × 2 × 𝐾 × 𝑠𝑙𝑜𝑝𝑒
1.6 × 10−19𝑒𝑉
Where 𝐸𝑔 is the energy gap
K= Boltzmann constant=1.38 × 10−23
Theory:TheenergygapEg of a materialisdefinedastheminimummountofenergyrequiredby
anelectrontoget excitedfromthetopof the valencebandtothebottomofconductionband.The
energygapincaseofametaliszeroandincaseofinsulatoritisveryhighinfeweV.Theenergy
gapofthesemiconductorsislessandliesbetweenthemetalsandinsulators.Thevariationof
resistanceofasemiconductor withtemperatureisgivenby
𝑹 = 𝑹𝟎 𝐞𝐱𝐩 𝑬𝒈
𝒌𝑻
Where‘R0’istheresistanceofthesemiconductoratabsolutezero,‘k’istheBoltzmannconstant
and‘T’is theabsolutetemperatureofthematerial
Procedure:
Connectionsaremadeasperthecircuitdiagram.Poursomeoilinthecopper
vessel.FixthediodetotheBakelitelidsuchthatitisreversebiased.Bakelitelidisfixedtothe
coppervessel,aholeisprovidedonthe lidthroughwhichthethermometerisinsertedintothe
vessel.Withthehelpofheater,heatthecoppervesseltillthetemperaturereachesupto800C.Note
thecurrentreadingat800C,applysuitablevoltagesay1.5Vandnotethecorrespondingcurrent
withevery50Cfalloftemperature,tillthetemperaturereaches the roomtemperature.
18
To determine the energy gap of a semiconductor
S.No Temperature T (degrees)
Temperature T (Kelvin)
Saturation current 𝑰𝒔
𝐥𝐨𝐠𝟏𝟎 𝑰𝒔 1/TX10-3 (/Kelvin)
1 2 3 4 5
65 60 55 50 45
338 333 328 323 318
20 18 16 14 12
2.006 2.890 2.773 2.639 2.485
2.95 3.00 3.05 3.09 3.14
𝐸𝑔 =2.303 × 2 × 𝐾 × 𝑠𝑙𝑜𝑝𝑒
1.6 × 10−19 𝑒𝑉
From graph slope=
𝐸𝑔 =2.303 × 2 × 𝐾 × 1595
1.6 × 10−19 𝑒𝑉
19
Precautions:
1. The current flow should not be too high in order to avoid the device from damaging.
2. The connections should be checked thoroughly.
Results:Theenergygapofagivensemiconductor is__0.6330 eV
20
21
Experiment -5
Numerical Aperture
Aim:The aim of the experiment is to determine the numerical apertur and acceptance angle of the
optical fibers available.
Equipment: 1.Numerical Aperture Kit 2.One meter PMMA fiber patch card 3.Inline SMA
adaptors 4.Numerical Aperture Measurement Jig
Formulae:NA = sinөmax = 𝑤
(4𝐿2+𝑊2)
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 the refractive index of the incident medium
and the sine of the maximum ray angle.
NA = ni.sinөmax; ni for air is 1, hence NA = sinөmax
For a step-index fibre, as in the present case, the numerical aperture is given by
N=(Ncore2 –ncladding
2)1/2
For very small differences in refractive indices the equation reduces to
NA = ncore (2∆)1/2
, where ∆ is the fractional difference in refractive indices. I and record
the manufacture‟s NA, ncladding and ncore, and ө.
BLOCK DIAGRAM:
Procedure:The schematic diagram of the numerical aperture measurement system is shown
below and is self explanatory.
Step1: Connect one end of the PMMA FO cable to Po of LED and the other end to the NA Jig, as
shown.
Step2: Plug the AC mains. Light should appear at the end of the fiber on the NA Jig. Turn the Set
Po knob clockwise to set to maximum Po. The light intensity should increase.
Step 3: Hold the white scale-screen, provided in the kit vertically at a distance of 15 mm (L) from
the emitting fiber end and view the red spot on the screen. A dark room will facilitate good
contrast. Position the screen-cum-scale to measure the diameter (W) of the spot. Choose the
largest diameter.
Step: 4 Compute NA from the formula NA = sinөmax = W/(4L2 +W
2)1/2
. Tabulate the reading and
repeat the experiment for 10mm, 20mm, and 25mm distance.
22
OBSERVATIONS:
To determine the numerical aperture of an optical fiber
S. No W (mm) L(mm) NA ө (degrees)
1
2
3
4
5
10
20
30
40
50
10
20
39
51
64
0.477
0.477
0.358
0.365
0.363
26033’4.93’
26033’4.93’’
20058’38.71’’
21024’27.7’’
21017’4.38’’
Total :1.98
Average value of numerical aperture NA=0.396
Average value of acceptance angle =
23
Step5: In case the fiber is under filled, the intensity within the spot may not be evenly distributed.
To ensure even distribution of light in the fiber, first remove twists on the fiber and then wind 5
turns of the fiber on to the mandrel as shown. Use an adhesive tape to hold the windings in
position. Now view the spot. The intensity will be more evenly distributed within the core.
Results:The determined numerical aperture and acceptance angle of the given optical fiber cable
are__0.396_
24
25
Experiment-6
Diffraction at a Single slit (LASER)
Aim:To determine slit width of single slit by using Laser Diode.
Apparatus: Laser Diode, Single Slit, Screen, Scale, tape etc.
Formula:-
𝒂 𝒔𝒊𝒏 = 𝒎
where a = width of the slit
m = order
= wave length of incident laser light
= angle
For small values of
sin tan = y
L
Theory:If the waves have the same sign (are in phase), then the two waves constructively
interfere, the net amplitude is large and the light intensity is strong at that point. If they have
opposite signs, however, they are out of phase and the two waves destructively interfere: the net
amplitude is small and the light intensity is weak. It is these areas of strong and weak intensity,
which make up the interference patterns we will observe in this experiment. Interference can be
seen when light from a single source arrives at a point on a viewing screen by more than one path.
Because the number of oscillations of the electric field (wavelengths) differs for paths of different
lengths, the electromagnetic waves can arrive at the viewing screen with a phase difference
between their electromagnetic fields. If the Electric fields have the same sign then they add
constructively and increase the intensity of light, if the Electric fields have opposite signs they add
destructively and the light intensity decreases.
Diffraction at single slitcan be observed when light travels through a hole (in the lab it is usually
a vertical slit) whose width, a, is small. Light from different points across the width of the slit will
take paths of different lengths to arrive at a viewing screen. When the light interferes
destructively, intensity minima appear on the screen.
For a rectangular slit it can be shown that theminima in the intensity pattern fit the formula
asin = m
26
Observations:
Distance between screen and slit L = 220 cm
Wavelength of incidence laser =6800x10-8
cm
Diffraction
Order, m
Distance between Minimas
X (cm)
y=X/2
(cm)
θ = sin θ
= tan θ= y/L A=
𝑚𝜆
𝑠𝑖𝑛𝜃 (cm)
1
2
3
4
5
2.6
5
7.1
9.6
11.6
1.3
2.5
3.55
4.8
5.8
5.9091x10-3
0.011x10-3
0.0161x10-3
0.01218x10-3
0.02636x10-3
0.0111
0.0116
0.0122
0.0121
0.0100
Total :-0.057
Average = 𝑇𝑜𝑡𝑎𝑙
5=0.0114 cm
27
Where m is an integer (±1, ±2, ±3….. ), a is thewidth of the slit, is the wavelength of thelight
and is the angle to the position on thescreen.The mth
spot on the screen is called the mth
order
minimum. Diffraction patterns for other shapes of holes are more complex but also result from the
same principles of interference.
Small Angle Approximation:
The formulae given above are derived using the small angle approximation. For small angles
(given in radians) it is a good approximation to say that sin tan (for in radians). For the
figures shown above this means that sin tan = y
L
Procedure:Diffraction at single slit
The diffraction plate has slits etched on it of different widths and separations. For this part
use the area where there is only a single slit.For two sizes of slits, examine the patterns formed by single
slits. Set up the slit in front of the laser. Record the distance from the slit to the screen, L. For each of the
slits, measure and record a value for y on the viewing screen corresponding to the center of a dark
region. Record as many distances, y, for different values of m as you can. Use the largest two or three
values for m which you are able to observe to find a value for a. The laser source has a wavelength of
6600x10-8
cm.Pull a hair from your head. Mount it vertically in front of the laser using a piece of tape.
Place the hair in front of the laser and observe the diffraction around the hair. Use the formula above to
estimate the thickness of the hair, a. (The hair is not a slit but light diffracts around its edges in a similar
fashion.) Repeat with observations of your lab partners' hair.
Repeat for one more slit width.
Precautions:Look through the slit (holding it very close to your eye). See if you can see the effects of
diffraction. Set the laser on the table and aim it at the viewing screen.
Note:DO NOT LOOK DIRECTLY INTO THE LASER OR AIM IT AT ANYONE! DO NOT LET
REFLECTIONS BOUNCE AROUND THE ROOM.
Result:The determined width of a singleSlit is0.0114 cm.
28
29
Experiment-7
Diffraction at a Double slit (LASER)
Aim: To determine slit width of double slit by using He-Ne Laser.
Apparatus: He-Ne laser/Diode Laser, Double Slit, Screen, Scale, tape etc.
Formula:-
𝒂 𝒔𝒊𝒏 = 𝒎
where a = width of the slit
m = order
= wave length of incident laser light
= angle
For small values of
sin tan = y
L
Theory:If the waves have the same sign (are in phase), then the two waves constructively interfere,
the net amplitude is large and the light intensity is strong at that point. If they have opposite signs,
however, they are out of phase and the two waves destructively interfere: the net amplitude is small
and the light intensity is weak. It is these areas of strong and weak intensity, which make up the
interference patterns we will observe in this experiment. Interference can be seen when light from a
single source arrives at a point on a viewing screen by more than one path. Because the number of
oscillations of the electric field (wavelengths) differs for paths of different lengths, the
electromagnetic waves can arrive at the viewing screen with a phase difference between their
electromagnetic fields. If the Electric fields have the same sign then they add constructively and
increase the intensity of light, if the Electric fields have opposite signs they add destructively and the
light intensity decreases.
Two-slitDiffraction:When laser light shines through two closely spaced parallel slits each slit
produces a diffraction pattern. When these patterns overlap, they also interfere with each other. We
can predict whether the interference will be constructive (a bright spot) or destructive (a dark spot) by
determining the path difference in traveling from each slit to a given spot on the screen.
30
Observations:
Distance between screen and slit L =230 cm
Wavelength of incidence laser =6800x10-8
cm
Diffraction
Order, m
Distance between Minimas
X (cm)
y=X/2
(cm)
θ = sin θ
= tan θ= y/L A=
𝑚𝜆
𝑠𝑖𝑛𝜃 (cm)
1
2
3
4
5.6
9
15
21.1
2.8
4.5
7.5
10.55
0.0121
0.0196
0.0326
0.04857
0.0558
0.06951
0.0625
0.0592
Total :-0.24701
Average = 𝑇𝑜𝑡𝑎𝑙
5=0.061753
31
Intensity maxima occur when the light arrives in phase with an integer number of wavelength
differences for the two paths: dsin = m
where m = ±0, ±1, ±2,… …and the interference will be destructive if the path difference is a half-
integer number of wavelengths so that thewaves from each slit arrive out of phase withopposite
signs for the electric field.
1sin
2d m
where m = ±0, ±1, ±2,… …
Small Angle Approximation: The formulae given above are derived using the small angle
approximation. For small angles (given in radians) it is a good approximation to say that
sin tan (for in radians). Form the figures that sin tan = y
L
Procedure:
Part B: Two-slit Diffraction
Using the two-slit templates, observe the patterns projected on the viewing screen.
Observe how the pattern changes with changing slit width and/or spacing.
For each set of slits, determine the spacing between the slits by measuring the distances between
minima on the screen. (The smaller spacings give are from the two slits patterns interfering, if
they get too small to measure accurately, just make your best estimate.) You will need to record
distances on the screen y and the distance from the slits to the screen, L.
Pull a hair from your head. Mount it vertically in front of the laser using a piece of tape.
Place the hair in front of the laser and observe the diffraction around the hair. Use the formula
above to estimate the thickness of the hair, a. (The hair is not a slit but light diffracts around its
edges in a similar fashion.) Repeat with observations of your lab partners' hair.
Precautions: Look through the slit (holding it very close to your eye). See if you can see the
effects of diffraction. Set the laser on the table and aim it at the viewing screen.
Note: DO NOT LOOK DIRECTLY INTO THE LASER OR AIM IT AT ANYONE! DO
NOT LET REFLECTIONS BOUNCE AROUND THE ROOM.
Results:The determined width of a DoubleSlit is 0.061753cm
32
Observations:Numberoflinesongrating per cmN= 15000/2.54lines/cm = 5905.5 lines / cm
Table:Determinationofwavelengthoflaserlight.
S.No.
Distance
betweengra
ting and
screen
D(cm)
Dif
fracti
on
Ord
ern
Distanceofthediffractedspotfromcentralmaxi
mum(cm)
θ=
Tan-
1(d
/D)(
deg
rees)
sinNn
(cm)
leftside
dL
rightside
dR
Mean d =
𝑑𝐿 + 𝑑𝑅
2
1
7 1 2.8 2.8 2.8 21048‟5.07‟‟ 6.2889x10
-5
2 8.7 9 8.85 51039‟26.63‟‟ 6.6405 x10
-5
2
12.2 1 5.3 5.2 5.25 23017‟0.81‟‟ 6.6934 x10
-5
2 15.3 15.8 15.55 51053‟0.52‟‟ 6.6612 x10
-5
3
16.5 1 7.3 7.2 7.25 23043‟13.42‟‟ 6.8118 x10
-5
2 21.5 21.6 21.5 52033‟36.43‟‟ 6.7225 x10
-5
Total=3.9878x10-5
Average λ=6.6447 x10-5
cm
=6644.7Å
33
Experiment-8
Wavelengthoflaserlight-Diffractiongrating
Aim:Todeterminethewavelengthoflaserbeamusingdiffractiongrating.
Apparatus:Lasersource(Diodelaser),Diffractiongrating,Opticalbench,Screen,Meterscale.
Formula: Wavelengthofalaser, sinNn
Where istheangleofdiffraction,
nistheorderofdiffractionpatternand
Nisthenumberoflinespercmongrating.
Procedure:
Arrangelasersource,diffractiongratingandscreenrectilinearlyatthesameheightontheopticalbench.
Keepthedistance(D)betweenthegratingandthescreenatafixedvalue(say70cm).Switchonthelasersourcesot
hatthelaserbeamincidentnormallyonthesurfaceofgrating.Thenlaserbeamgetsdiffractedfromtheruledsurfa
ceofgratingandformadiffractionpatternonthescreen.Wecanobservedifferentdiffractionordersofbrightspo
tsonthescreenoneithersideofthecentralmaximum.Nowmeasurethedistancebetweenthespotsofthesameord
erfromthecentralmaximum.Letthedistancefromthecentralmaximumtodiffractedspotonleftsideisd1andth
atontherightsideisd2.Theaverageofd1andd2isd(say).Thewavelengthofthegivenlaserbeamcanbedetermin
edusingtheformula.
RepeattheexperimentfordifferentvaluesofDandnotethecorresponding„d‟valuesfordifferentdiffractionord
ersandtabulatethereadings.
Precautions:
1. Lasersource,diffractiongratingandscreenshouldberectilinearatthesameheight.
2. Thelaserlightshouldnotbeseendirectly.
3. Laserlightshouldincidentnormallyonthesurfaceofthegrating.
Results:Thewavelengthofgivenlaserisdeterminedasλ==6644.7Å
N
34
Normal incident procedure
Measurement of λ:-
35
EXPERIMENT 9
“DIFFRACTION OF GRATING – NORMAL INCIDENCE METHOD”
Aim:-
To determine the wavelength of a given source of light by using the diffraction grating in the normal incidence method.
Apparatus: Grating, Spectrometer, Spirit level, Reading lens, Sodium vapour lamp.
Formula:-
𝑛𝑁𝜆 = sin𝜃
𝜆 =sin 𝜃
𝑛𝑁𝐴0
Where ‘’ = the wave of the light source
= Angle of diffraction.
‘n’ = Order of the spectrum
‘N’= Number of lines per centimeter =15000/2.54 = 5905 Least count:
𝑙𝑒𝑎𝑠𝑡 𝑐𝑜𝑢𝑛𝑡 (𝐿.𝐶) =𝑜𝑛𝑒 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒 𝑜𝑛 𝑚𝑎𝑖𝑛 𝑠𝑐𝑎𝑙𝑒
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠 𝑜𝑛 𝑣𝑒𝑟𝑛𝑖𝑒𝑟 𝑠𝑐𝑎𝑙𝑒
If the vernier scale contains 30 divisions
𝑙𝑒𝑎𝑠𝑡𝑐𝑜𝑢𝑛𝑡 ==30′
30= 1′
The primary adjustments of spectrometer
a) Eye – Piece: The telescope is turned towards a white surface i.e., wall and the
Eye-piece is moved in (or) out until the cross-wires are seen clearly. Adjust the one
cross wire into vertical by rotating the eye piece.
b) Telescope:The Telescope is directed towards a long distant object and adjusts the
telescope until the distance object is clearly seen without parallax error. Now the
telescope is ready to receive a parallel beam of light.
c) Collimator: The slit of the collimator is illuminated with sodium light. The telescope is
brought in line with the collimator and the distance of the slit from the collimating lens is
adjusted until a clear image of the slit with well defined edges is formed in the plane of
the cross wires without any parallax error. Slit is adjusted to be vertical and narrow.
d) Prism table: A sprit level is kept on the prism table parallel to the line joining to the
leveling screws. The two screws are adjusted until the air bubble of the spirit level comes
to the centre. Then the spirit level is turned on the table perpendicular to this position and
the third screw is adjusted until the air – bubble comes to the centre. Now the surface of
the prism table will be horizontal
36
To d
ete
rmin
e the
wavele
ngth
of a
giv
en lig
ht sourc
e
𝝀=𝒔𝒊𝒏
𝜽
𝑵 𝒏
𝑨𝟎
57
00
20
Me
an
𝑷
+𝑸
𝟐
()
20
Ve
r -
R
Dif
fer.
„Q‟
20
Ve
r -
L
Dif
fer
„P‟
20
Sp
ec
tro
me
ter
Re
ad
ing
s
Te
les
co
pe
on
Rig
ht
sid
e
Ver-
R
𝑽𝑹𝑹
0
Ver-
L
𝑽
𝑹𝑳
18
0
Te
les
co
pe
on
Le
ft s
ide
Ver-
R
𝑽𝑳𝑹
20
Ver-
L
𝑽𝑳𝑳
20
0
Line yell
ow
Spectrum Order „n‟
1
Procedure:-
Normal Incidence:
The slit of the spectrometer is illuminated with sodium vapour lamp. The
telescope is placed in line with the axis of the collimator and the direct image of the slit is
observed. The slit is narrowed and the vertical cross-wire is made to coincide with the
centre of the image of the slit. The reading of one of the vernier isadjusted for 0 – 0
position. The prism table is clamped firmly and the telescope turned through exactly 900
and fixed in position. The grating is held with the rulings vertical and mounted in its
holder on the prism table such that the plane of the grating passes through the centre of
the table and the ruled surface towards the collimator. The prism table is released and
rotated until the image of the slit is seen in the telescope on the ruled side of the grating.
The prism table is fixed after adjusting the point of intersection of the cross-wires is on
the image of the slit. Then the vernier table is released and rotated through exactly 450
from this position so that the ruled side of grating faces the collimator. The vernier table
is fixed in this position and the telescope is brought back to the direct reading position.
Now the light from the collimator strikes the grating normally.
Measurement of:
When we will rotate the telescope, we observed the two yellow colour lines
very close to each other on either side (left and right sides); they are called ‘D1’ and
‘D2’ lines. The point of intersection of the cross wires is set on the yellow line and its
readings is noted on both the verniers. Similarly the reading corresponding to the
other side (i.e., right side) and similarly the readings corresponding to yellow line of
the first order spectrum are noted. Half the difference in the readings corresponding
to any one line gives the angle of diffraction () for that lines in the first order
spectrum.
The experiment is repeated for the second order spectrum. The number of lines
per cm of the grating (N) is noted and the wavelength ‘’ of the spectral line is found by
relation. nN
sin
Precautions:
Always the grating should be held by the edges. The ruled surface should not be
touched.
(1) Light from the collimator should be uniformly incident on the entire surface of the
grating.
Result:
The determined wave length of the given light source by using the diffraction of
grating in the normal incidence method is ---------------A0.
Collimator
Prism
table
Prism
Telescope
Collimator
Telescope
Experimental arrangement Direct reading
Experiment- 10
Dispersive Power of a Prism
Aim: To determine the dispersive power of a material of prism using Spectrometer
Apparatus:Spectrometer, Prism, Mercury Vapor Lamp etc.
Formula:
The dispersive power (𝜔) =𝜇𝐵𝑙𝑢𝑒−𝜇𝑦𝑒𝑙𝑙𝑜𝑤
𝜇𝑎𝑣𝑔−1
Where that𝜇𝑎𝑣𝑔 =𝜇𝐵𝑙𝑢𝑒 +𝜇𝑦𝑒𝑙𝑙𝑜𝑤
2
Refractive index of the prism for the particular colour
𝜇 =sin
𝐴+𝐷𝑚𝑖𝑛
2
sin 𝐴
2
𝜇𝑟𝑒𝑑 =sin
𝐴+𝐷min (𝑦𝑒𝑙𝑙𝑜𝑤 )
2
sin 𝐴
2
&𝜇𝑏𝑙𝑢𝑒 =sin
𝐴+𝐷min (𝑏𝑙𝑢𝑒 )
2
sin 𝐴
2
Where A is the angle of the prism
minD is the angle of minimum deviation of particular colour.
Where A is a angle of the prism = 600
Least count:
𝑙𝑒𝑎𝑠𝑡𝑐𝑜𝑢𝑛𝑡 (𝐿.𝐶) =𝑜𝑛𝑒𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑣𝑎𝑙𝑢𝑒𝑜𝑛𝑚𝑎𝑖𝑛𝑠𝑐𝑎𝑙𝑒
𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠𝑜𝑛𝑣𝑒𝑟𝑛𝑖𝑒𝑟𝑠𝑐𝑎𝑙𝑒
If the vernier scale contains 30 divisions
𝑙𝑒𝑎𝑠𝑡𝑐𝑜𝑢𝑛𝑡 ==30′
30= 1′
Theory: A spectrometer is used to measure the necessary angles. The spectrometer consists of
three units: (1) collimator, (2) telescope, and (3) prism table. The prism table, its base and
telescope can be independently moved around their common vertical axis. A circular angular
scale enables one to read angular displacements (together with two verniers located diametrically
opposite to each other).In the experiment, we need to produce a parallel beam of rays to be
incident on the prism. This is done with the help of a collimator. The collimator has an adjustable
rectangular slit at one end and a convex lens at the other end.
Colour Position of scale
M.S.R „a‟
V.S.C
V.S.C x LC „b‟
Spectrometer Total reading
„a+b‟
Blue Left
Right
139
319
30
30
30‟
30‟
𝑽𝑳 =139030‟
𝑽𝑹 =319030‟
Yellow Left
Right
141
321
0 0
0‟
0‟
𝑽𝑳 =1410
𝑽𝑹 =3210
Direct reading
Left
Right
180
360
0 0
0‟
0‟
𝑽𝑳′ =180
0
𝑽𝑹′ =360
0
When the illuminated slit is located at the focus of the lens, a parallel beam of rays emerges from
the collimator. We can test this point, with the help of a telescope adjusted to receive parallel rays.
We first prepare the telescope towards this purpose as follows:
Setting the eyepiece:Focus the eyepiece of the telescope on its crosswires (for viewing the
crosswires against a white background such as a wall) such that a distinct image of the crosswire
is seen by you. In this context, remember that the human eye has an average “least distance of
distinct vision” of about 25 cm. When you have completed the above eyepiece adjustment, you
have apparently got the image of the crosswire located at a distance comfortable for your eyes.
Henceforth do not disturb the eyepiece.
Setting the Telescope:Focus the telescope onto a distant (infinity!) object. Focusing is done by
changing the separation between the objective and the eyepiece of the telescope. Test for the
absence of a parallax between the image of the distant object and the vertical crosswire. Now the
telescope is adjusted for receiving parallel rays. Henceforth do not disturb the telescope focusing
adjustment.
Setting the Collimator:Use the telescope for viewing the illuminated slit through the collimator
and adjust the collimator (changing the separation between its lens and slit) till the image of the
slit is broughtto the plane of cross wires as judged by the absence of parallax between the image
of the slit and crosswires.
Optical leveling of the Prism:
The prism table would have been nearly leveled before use have started the experiment. However,
for your experiment, you need to do a bit of leveling using reflected rays. For this purpose, place
the table with one apex at the center and facing the collimator, with the ground (non-transparent)
face perpendicular to the collimator axis and away from collimator. Slightly adjust the prism so
that the beam of light from the collimator falls on the two reflecting faces symmetrically. When
you have achieved this lock the prism table in this position. Turn the telescope to one side so as to
receive the reflected image of the slit centrally into the field of view. This may be achieved by
using one of the leveling screws. The image must be central whichever face is used as the
reflecting face. Similarly, repeat this procedure for the other side.
Finding the angle of the prism (A):With the slit width narrowed down sufficiently and prism
table leveled, lock the prism table and note the angular position of the telescope when one of the
reflected images coincides with the crosswires. Repeat this for the reflected image on the
otherside (without disturbing the prism and prism table). The difference in these two angular
positions gives 2a.
To d
ete
rmin
e re
fractive index o
f a g
iven p
rism
Refr
active Index
𝝁=𝒔𝒊𝒏 𝑨
+𝑫𝒎𝒊𝒏
𝟐
𝒔𝒊𝒏 𝑨𝟐
1.5
46
5
1.5
20
8
Cal
cula
tio
ns:
- 𝝁
𝒂𝒗𝒈
=𝝁𝑩𝒍𝒖𝒆
+𝝁𝒓𝒆𝒅
𝟐=
1.5
33
65
The
dis
pe
rsiv
e p
ow
er
(ω)
of
a g
iven
prism𝝎
=𝝁𝑩𝒍𝒖𝒆−𝝁𝒓𝒆𝒅
𝝁𝒂𝒗𝒈−𝟏
=0
.04
81
5
ME
AN
𝑃
+𝑄
2
(𝑫𝒎𝒊𝒏
)
41
03
0’
39
0
An
gle
of
Min
imu
m
Dev
iati
on
𝑽𝑹
~𝑽𝑹
′ 𝑄
41
03
0’
39
0
𝑽𝑳~𝑽𝑳
′ 𝑃
41
03
0’
39
0
Dir
ec
t R
ea
din
g
Ve
r-R
𝑉 𝑅′
36
00
Ve
r-L
𝑉 𝐿′
18
00
Sp
ec
tro
mete
r
Rea
din
gs
Ve
r-R
𝑽𝑹
31
9030
‟
32
10
Ver-
L
𝑽𝑳
13
9030
‟
14
10
colour
Blu
e
yello
w
Finding angle of minimum deviation (Dm):
Unlock the prism table for the measurement of the angle of minimum deviation ( Dm). Locate the
image of the slit after refraction through the prism as shown in
. Keeping the image always in the field of view, rotate the prism table till the position where the
deviation of the image of the slit is smallest. At this position, the image will go backward, even
when you keep rotating the prism table in the same direction. Lock both the telescope and the
prism table and to use the fine adjustment screw for finer settings. Note the angular position of
the prism. In this position the prism is set for minimum deviation. Without disturbing the prism
table, remove the prism and turn the telescope (now unlock it) towards the direct rays from the
collimator.
Note the scale reading of this position. The angle of the minimum angular deviation, viz, Dm is
the difference between the readings for these last two settings.
Principle:Refractive Index (µ): It is defined as
µ = velocity of light in vaccum
velocity of light in air
And
sinsin 2
sinsin
2
mA D
i
Ar
Where A Angle of Prism
Dm Angle of minimum deviation
Dispersive power ( w ):- Angular rotation for a given wavelength is called dispersive power of
the material of a prism
(𝜔) =𝜇𝐵𝑙𝑢𝑒 −𝜇𝑦𝑒𝑙𝑙𝑜𝑤
𝜇𝑎𝑣𝑔− 1
Where that𝜇𝑎𝑣𝑔 =𝜇𝐵𝑙𝑢𝑒 +𝜇𝑦𝑒𝑙𝑙𝑜𝑤
2
Precautions:
1. Take the readings without any parallax errors
2. The focus should be at the edge of green and blue rays
Results: -The dispersive power of the given prism is 0.04815
Verification of First Law: 𝑛. 𝑙 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Tension applied to the wire = T = _______________ dyne
Linear Density of the -------------------- wire (m) = ________________ gm/cm
S.No Frequency of
Tuning Fork ‘𝒏’ (Hz)
Resonating Length ‘𝒍’ of vibrating Segment (cm) 𝒏. 𝒍
Trail – I Trail – II Mean (𝒍)
1.
2.
Experiment: 11
“SONOMETER EXPERIMENT”
Aim: To verify the laws of vibrations of stretched strings. Apparatus: Sonometer, a half kilogram weight hanger, with suitable hanging weights, a Rubber hammer, tuning forks of different frequencies, steel, plastic, copper wires. Formula:
A stretched string plucked at its middle and released. It vibrates in a single loop which is the fundamental mode of the frequency ‘n’ depending upon the tension (T), the length of the vibrating loop (l) and the mass per unit length (m) of the wire.
The relation connecting l, T & m is given by
m
T
ln
2
1
From the above equation the laws of transverse vibrations of a stretched strings are stated as
(1) The frequency of stretched string is inversely proportional to its length (l). T& ‘m’ are being constants.
ln
1 constantnlor
(2) The frequency of the stretched string is directly proportional to the square root of the tension (T) ‘m’ & ‘l’ being constants.
T
n 2
constant
(3) The frequency of stretched sting is inversely proportional to square root of its linear density. ‘T’ & ‘l’ are constants.
orm
n1
n2m = constant
Description: A sonometer consists of a hallow rectangular box of about 125 cm long and 15 cm broad made of teak wood and covered with thin plate or plank of soft wood. The box is provided with two long fixed knife edges parallel to its breadth. At one end two or three legs are provided to which strings of various materials and radii can be firmly attached. These materials can be passed over the fixed knife edges. Resonance takes place when the frequency of external body (tuning fork) is equal to natural frequency of segment of the wire. At resonance energy transfer from external body takes place and the segment of wire between the knife edges vibrates with maximum amplitude. Procedure: Verification of first Law: Suitable number of weights are placed on weight hanger which is attached to one end of the sonometer wire to create sufficient tension in the wire. One of the tuning forks is excited by the rubber hammer and the stem of the tuning fork is set vertically on the top of sounding box. The length of the wire between the knife edges is adjusted slowly by moving knife edges nearer to one another or apart. A small and light V-shaped paper rider is placed at the middle of the string. The length of the wire is adjusted until the paper rider flutters vigorously and falls down. In this position, the natural frequency of the vibrating segment of the string is equal to the frequency of the tuning fork. The length ‘l’ of the vibrating segment of the string is measured.
orTn
Verification of Second Law:
consantl
T
2
Frequency of the tuning fork n = ___________ Hz
Linear density of the ---------------- wire m = ____________ gm/cm
S. No Tension (T) applied in
(gm wt)
Resonating length of wire (𝒍) with the given tuning fork (cm)
2l
T
Trail – I Trail – II Mean (𝒍)
1.
2.
Verification of Third Law:𝑚𝑙2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
The product (ml2) is constant when ‘n’ & ‘T’ are constant.
Frequency of tuning fork n = ___________ Hz
Tension applied T = mg = ___________ dyne
S. No Type of
wire
Linear density m
(gm/cm)
Resonating length of the wire ‘𝒍’ with the given tuning fork (cm) 𝒍𝟐𝒎 Trail – I Trail – II Mean (𝒍)
1.
2.
Keeping the tension constant and using the same wire, the experiment is repeated
with different tuning forks and the results are tabulated as shown in figure. Thus first law is verified by showing that 𝑛𝑥𝑙 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. Verification of Second Law: To verify the second Law, a tuning fork and same type of wire is used throughout the experiment. The tension is applied to wire and the experiment is repeated with different tensions and the observations are tabulated.
The ratio 2l
T is constant where ‘m’ and ‘n’ are constants. Thus second law is
verified showing 2l
T = constant.
Verification of Third Law: To verify the third law, three wires of different linear densities (m) are taken and a Tension ‘T’ is applied. A tuning fork is exited and the stem of its is placed by the side of the wire and the resonating length of the wire is noted. Using the same tuning fork, and the same tension, the experiment is repeated with different materials of wires and observations are tabulated.
Precautions:
1. When the tuning fork is placed on the sounding box vertically, it should not touch
the sonometer wire.
2. The length of the wire between the knife edges is slowly varied.
3. The paper rider should be always at the centre of the segment.
4. The pulley should be frictionless
Result :
The laws of vibrations of stretched strings are verified.
Experiment 12
“MELDE’S EXPERIMENT”
Aim:
To determine the frequency of a vibrating bar or tuning fork using Melde’s arrangement
Apparatus:
Storage cell eliminator, plug keys, connecting wires, Meter scale, thread, card, weight
and electrically maintained tuning fork.
Formula:
The formula for the frequency of the transverse wave is
𝑛 =1
2 𝑇
𝑙 .
1
𝑚 (1)
The formula for the frequency of the longitudinal wave is
𝑛 = 𝑇
𝑙 .
1
𝑚 (2)
Where T = tension in thread =(M1+M2)g
M1 = Load applied to pan
M2 =Mass of card board pan
𝑔= acceleration due to gravity
𝑙 =The length of the single loop
𝑚 = Mass per unit length of thread
Description:
An electrically maintained tuning fork consists of electro magnet between the two
prongs of tuning fork without touching either of the prongs as shown in figure. To one of the
prongs a thin brass plate with an adjustable screw is riveted on it. By adjusting the screw,
contact is established with the thin brass plate.
Electrical connections are made as shown in figure 1. When plug is inserted the circuit is
completed and electrical current flows through the circuit. Energizing the electromagnet by
pulling both the prongs in inward, the circuit is broken immediately at the points, the
electromagnet loses its magnetism and the prongs fly back to its original position. Consequently
contact is once again established at the circuit and the process repeats automatically.
One end of the thin thread is connected to a small screw provided on one of the prongs
of the tuning fork. The other end of the thread is connected to a light card board pan and the
material of the thread is passed on a small friction free pulley fixed on to a stand kept at a
distance of 3 to 4 m from the fork.
Small weight is placed on card board pan so that sufficient tension is created to the
string. The tension in the string can be attached by changing the weights in the card board pan.
Transverse Arrangement:
Mass of card board pan M2 = Mass per unit length of thread m = To determine the frequency of transverse waves
S.N
o
Load
ap
plie
d t
o p
an
M1 (
gm)
Ten
sio
n T
=(
M1+M
2)g
dyn
e
No
. of
loo
ps
(x)
Len
gth
of
‘x’ l
oo
ps
d (
cm)
Len
gth
of
each
loo
p
l =
d/x
cm
𝑻
dyn
e
cmdynel
T/
1.
2.
3.
4.
Total:
Average value:
The average of l
Tis substituted in equation 1 and frequency is calculated.
Average of l
T= ___________ dyne / cm =
This value is substituted in equation (1) then
𝑛 =1
2 𝑇
𝑙 .
1
𝑚 𝐻𝑧
n=
Procedure:
For transverse arrangement
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.
The apparatus is first arranged for transverse mode of vibrations with length of
the string 3 to 4 cm and passing it over the pulley, the electric circuit is closed and the rheostat is
adjusted till the fork vibrates steadily. The string starts vibrating with a frequency exactly half
the frequency of the fork. The load in the card board pan is adjusted slowly, till a convenient
number of loops with defined nodes and maximum amplitude at the antinodes are formed. The
vibrations of string are being in the vertical plane.
The no. of loops (x) formed in the string between pulley and the fork is noted and the
length of the string (d) between the pulley and the fork is noted in table 1. The length (l) of a
single loop is calculated by
𝑙 =𝑑
𝑥 𝑐𝑚
Let M1 = mass of card board pan
M2 = load added into the card board due to gravity at place.
For Longitudinal arrangement
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.
The apparatus is first arranged for longitudinal mode of vibrations with length of the
string 3 to 4 cm and passing it over the pulley, the electric circuit is closed and the rheostat is
adjusted till the fork vibrates steadily. When the fork is placed in the longitudinal position and
the string makes longitudinal vibrations. . The string starts vibrating with a frequency exactly at
the frequency of the fork.
The load in the card board pan is adjusted slowly, till a convenient number of loops with
defined nodes and maximum amplitude at the antinodes are formed. The vibrations of string are
being in the same plane.
The no. of loops (x) formed in the string between pulley and the fork is noted and the
length of the string (d) between the pulley and the fork is noted in table 1. The length (2) of a
single loop is calculated by
𝑙 =𝑑
𝑥 𝑐𝑚
Let M2 = mass of card board pan
M1 = load added into the card board due to gravity at place.
Table – II:
Longitudinal Arrangement:
Mass of card board pan M2 = Mass per unit length of thread m = To determine the frequency of longitudinal waves
S.N
o
Lo
ad
ap
plie
d t
o p
an
M1 (
gm
)
Ten
sio
n T
=(M
1+
M2)g
(d
yn
e)
No
. o
f lo
op
s (
x)
Le
ng
th o
f „x
‟ lo
op
s
d (
cm
)
Len
gth
of
ea
ch
lo
op
l =
d/x
(c
m)
𝑻
(dyn
e)
cmdynel
T/
1.
2.
3.
Total:
Average value:
The average of l
Tis substituted in equation (2) and the frequency of fork is calculated.
Average of l
T= ___________ dyne / cm
This value is substituted in equation (2) then
𝑛 = 𝑇
𝑙 .
1
𝑚
n = ________________ Hz
Result:
The determined frequency of a tuning fork using Melde’s arrangement is 𝑛 =
________________
