..'
In l1 u lion Manual EngineeringPhysics
(:?1)"·) UNl\fERSITV
IEM"s
..~~Of ENGINEERING U EM t{ 0 l t{ ATA br (Ot>b!rsh<-d
University
-1 Laboratory
own University
in Kolkata
& MANAGEMENT (UEM)
1n AO of Stm Gowt.. l rKOgnis.td i.'J 22 ~ UGC Act. t./..111~ ol Hru>. Govt. d lt-d.. l
Arca. Plot No. Ill - 8/5, New Town, Action Area - Ill, Kolkata - 700156
) ) )
UNIVERSITY OF ENGINEERING
-
AND MANAGEMENT
(UEM)
KOLKATA CAMPUS
CJ!'
University area,Plot
Department
No.111-8/5,New
Town.Actlon Area lll,kolkata-700156
of Basic Science and Humanities
--
'
'
... "'
Paper Name: Physics lab-I
)
Paper code: PH-191··
)
J
ODD SEMESTER
)
,,
.,
I '
, .., • r
.
'
-
Contents Experiment 1: Determination of Young's Modulus l. lntroduction:········································································~··············:····
.,-
1
2. Procedure
2
3. Observation table
3
4. Calculation
4
5. Error Analysis
4
6. Precaution & Discussion
:
4
Experiment 2: Newton's Ring Experiment
1. Introduction
5
2. Theory
6
3. Procedure
7
4. Observation Table
8
5. Error Analysis
9
6. Precaution & Discussion
9
)
Experiment 3: Rigidity Modulus by Static Method
-
1. Introduction
11
2. Procedure
12
-' _,,
JI
...._.
,
-
3. Observation Table
12-13
"
Experiment 4: Rigidity Modulus by Dynamic Method 1. Introduction .............•...............................................................................
15
2. Procedure
15
3. Observation Table
·
:
:
16
Experiment S: Optical Fibre Experiment
-
~
..-
l.lntroduction
17
2.Procedure
18
3. Observation Table
19
4. Discussion
19
Experiment 6: Carry Foster's Bridge l.lntroduction
20-22
2. Procedure
22
3. Observation Table
23
4. Error Analysis
24
5. Discussion
24
Experiment 7: Laser Diffraction 1.lntroduction
-.,
-..
.
-
,_
25
2. Procedure
26
3. Observation Table
27
4. Error Analysis
28
5. Discussion
28
Experiment 8: Angular Dispersive Power Of Prism 1. Introduction 2. Diagram
29 ~
:
3. Procedure 4. Observation Table
:
:
30 31-32 33-34
5. Calculation
35
5. Error Analysis
35
6. Precaution & Discussion
35
Experiment 9: Measurement of Thermal Conductivity by Lee's Method 1. Introduction
36-37
2. Procedure
38-39
3. Observation Table
39
4. Calculation
40
~
5. Error Analysis
40
~
6. Precaution & Discussion
40
~ ~
" :) ~ ~ ~ ~
, ~
~ ~ ~
,
lH 8Jl-
'' 0
fl UtC
l l
1
Lt· Hi
111 1\·1 ION (
d t("11lltnC th
r· Y )lJN , ~
Youns., s modulus ()(
IOD1JJ,IJS of
c-1,1\llCtl)'
lh
111:\ICll~tl
of,,,,,,,.
,, ,, .. ,
tn<'th d
If :l light b."'r-<'I brc:id1h.h :lnd deplh ti is placc<.J honzon1fllly on two "Knife edges separated t.Jy a d1s1ance L. nmt a load of mass m, ap_plicd at_!he mid-point of thcba~. produces;, dcpr -=:.JOn I of lhe ~r. then Young"s modulus Yof the material of rbe bar is given by
-
y
---
.
gL3
m
4bd3
l
-----
.
-
w..!!_crc g is the acceleration due to wvitt. This is the working formula of the experiment, and is vahd so long as tbe slope of the bar al any point with respect 10 the unstrained posit 10n as much less than unity. Herc Y is determined by measuring 1hc quanlities b, d, l and the mean ~ion _!_.£QITcs~nding_!.C?_ a load rn, _lf b, d, L and I arc measured in cm, m in. gm, g is expressed in cm/sec", aOd then Y is obtained in dync/cm2 in C.G.S.
PROCEDURE (i) Measure the length of the given bar with a meter scale and mark its mid-point. Draw marks on the scale corresponding to some length LI LI' of the bar {say 70 cm). (ii) Mount on the bar, rbe frame F carrying a knife-edge. Now place the bar with its leas1 dimension verucal, on the knife-edges NI and N2 such thal 1hc Lill' marks coincide with the knife-edges. Mount a spirit level on the bar and adjust the leveling screws until the bar JS horizontal.
,
/
/
6
(111)B1in ~rnr o trarn f>on1hccC'ntrol1i:rni;v 1~ rn.r~o(lt'Y'bar m1c1 ope ml vr ' the po.nrcr P Adju I 1h lcvcl1n1! screws ol rbe rmcroscop until 1h I o ie « r rfe ,,_ II
. \
edvv
l
rb
Placc
(1v tcrrmne the vernier constant of the microscope th J>O Ilion of the nucroscope on the vert_icill scnic
rh»
W11h zero loads on the hanger, record
,,. ( ) Pince a load or0.5 Kg on the hanger. This will produce a depression of the bar. Aller the rhcal posmon of the microscope until the image or pointer touches that of the horizontal
cross-wire. Nore again the vertical scale reading of the microscope. The difference of the two microscope R"ndings gives the depression of the bar for the load ofO.Skg
in steps of 0.5kg and at each observation, and at each step record the ven ica I scale reading of the microscope. Now decrease the load 10 zero in the same steps as used for increasing the load, and record Che corresponding vertical scale-readings of tbe microscope. Determine the mean of these two readings, and calculate the depression by subtracting the zero-load reading. (vi) Increasing gradually the load
)
' )
'.) ')
(vii) Remove the bar without disturbing the position of the stands, and measure accurately the 1) distance between the knife-edges (i.e. LI LI by placing vertically the marked face of a meter scale across the knife-edges. (viii) Determine the vernier constant of the slide callipers and measure with ii the breadth b of the bar at three different places. Calculate the mean breadth of the bar. Nole the zero error, if any, of the slide callipers and find the correct value of b,
) ~
(1x) Determine the least count of the screw gauge and measure depth d of the bar at a number of places along the length of the bar. Find the mean value. Note the zero error, if-any of the screw gauge and obtain the correct value of d.
j ~
)
(x) Draw a graph with the load m in gm along the X-axis and the corresponding depression I in cm along the Y-axis and determine the value of Y.
~
OBSERVATIONS
=>
Table-I : Determination
or the
Vernier Constant (v.c.) of the microscope
~
. ·~ . ·~
,
·~ ·~
·•~
·~ •. ,
Sc Divisions (say m) of the vernier scale=
I Value
.<:t.~.. divisions {say n) of the main scale .
of I smallest main Value- of I vernier (11 1) (cm) / scale divrsion i/1) ft?'
=:/
C
Vernier constant
vc
= (11
-
/2 )'(
cm)
Wflv
I
L __
- ---
--------
I""'~
.
(
"
.,
·l · I o. cl dcp1 c sro n cl:ll. fo1
l abl
hO\
()
n length
Dis1nncc between 1hc knife-edges L •
~
f
I obs
Load
\ hCl ,, ,·,"ll-C IC
Ill
hh·1.-n ... 1u~ IO:ld ICn>
{kg)
\l;l1 1
I
(~)
--.--,·,·11u<'1-
Tomi
ft· v)
• (v~
C.\k~)
Dcrrr ~<:1011 I 1c111)
<1111;? fOI
0
I:
0 a-. (1-b ~ ~1) a. c.
'.:\I ·(h)
05 ) 0
(~)
1·~
o:
2.
~
~
;.
0... - IL
Table-J : Vernier Constant (v.c.) or the slide calipers ..... Divisions of the vernier scale=
V"luc of I smallest main
scale division (Ii)
..
J
divisions of the main scale.
of I vernier (l2 = : 11) (cm) Value . ..
......
division
Vernier constant v.c. =-(I, -
... ..
t.,) (cm)
. .. ..
.:J :.J
Table-e : Measurement or breadth (b) of the bar by slide calipers No of obs
Reading\
(cm)
of
Main scale
Tora I
Mean b (cm)
reading b
the
Vernier
Zero error (cm)
Correct b (cm)
(cm)
Table-5 : Least count (L.C.) of the screw g:rnge Pitch of the screw p (cm)
No
of divisious n on the
Least count -
p'I\
(cru)
circutar scale
~~~~~-~
8
l
\
I 1hlr
6
1\lr1,111 C'l1lr111 of tlrpl h (d) of I h
' ... I "'' \
.
M nu d
I 1)tnl 1 cnd111 r/(c111)
Re .1.l111ll
l I "':i~ ~ I he
h:u by th(
/c>tO
(c111)
(
''
r•n11}~<'
t:l I \•I 111)
1)11"(.fr/ I 1..111)
_I
'~nle
(
_
' I
~
-·--'--------'-_,__________.. _ _____..__
- _l
CALClJLA TIONS Now draw a graph of Load (m) vs. Depression (I) m will be along X-axis and I will be along Y axis from the graph calculate the value of the slope (llm). Put the value of the inverse of rhe slope in rbe expression ofY. Herc Y is determined by measuring rbe quannnes b, d, l and the mean depression I corresponding to a load m, J f b, d, l and I arc measured in cm, m in gm, g is expressed in cm/scc2, and then Y is obtained in dyne/cm2 in C.G.S. Jn SJ. Y is obtained in New1on/m2 PRECAUTIONS (i)
The beam must be kept horizontal and the pointer along with the frame must be suspended at its !11id points.
(ii)
Since lhe value of depth (d) Ls small and it occurs 10 the third power in the expression for Y, it must be measured with a screw gauge.
(iii)
While raking rhc reading microscope must be rotated in the same direction , so as 10 avoid the back -lash error.
ERR.OR ANALYSIS y
=
gL3 4b
"'
The maximum proportional error in Y is thus
(
-" ~
= 3 oL + ob + 3 od + 01
oy) y
mnz
l
b
DiSCUSSJONS
9
•
d
I
\
NEvV
ON'S HJNG EXPERIMENT
ODJ£CTIVE
To _111dv the formation of Newrons nnas in the air-fihn in between a ptaoo-convcx lens nnd ~l:iss ~l:lt<.> usmg nearly monochromatic light from a sodium-source and hence 10 derermme the radius of curvature of the piano-convex lens
:i
APP.-\R,\ TUS
."'\nearly monochromatic source of lighi (source of sodium light) A piano-convex Jens An optically Oat glass plates
• • ,~
convex lens A uavetling microscope A
THEORY
,.,.. ) I~
FU!. 2. Newton's tines
·~
·~
·~ ~
:)
When a parallel beam of monochromatic light is incident nonnally on a combination of a piano-convex lens Land a glass plate G, as shown in Fig. I, a part of each incident ray is reflected from the lower surface of the lens, and a part, after refraction through the air film between the lens and the plate, is reflected back from lhe plate surface. These two reflected rays are coherent hence they wiJJ interfere and produce a system of alternate dark and brighr rings with the point ofcontact between the Jens and the plate as the center. These rings are known as Newton's ring.
~
For a normal incidence of monochromatic light, the path difference between the reflected rays (see Fig. J) is very nearly equal to 2 1 where and 1 are the refractive index and thickness of the air-film respectively, The fact that the wave is reflected from air to glass
~
Therefore, IOr bright fringe
~
I
Zµ t=(n+z) A; n ""0.1.L3
~ and for dark fringe ~ ~
4 ~
10
(I)
'"I
I"
,,).
0,
1,}
(J)
\
(J) whe1~D11
tht>tt1r.mc1e1of1hcnthr111 nn)reduces 10
of the low r sur l.u c
ol1he plnno convex lcn
~
..
D,; :: StR
E
/:
/
-,
.
I
.\
(4)
\
:
) - ·-~
~
.s-:
'l
·~
/A
./
D
Fig.1G~b)'~ed11'.\
~
di!?t;it~
Ch(a
hdrn~c; alt~ dS'-'*"n
l
From equations (1) and (4), we get,
·l
D,.
1
(
=
1\).R +) / · for n-lb bright ring -
~
o I .......
'l
., ~
(5)
µ
1y·R
(
=4n•n:+-;
fly
"
(n ~m).lh 11"~l
nne
(~
Similarly, from equations (2) and (4), we obtain
~
D_
~
1
4nlR s::
•
•'
(T)
for It -th dar\: ring
~
1
:)
:1
D ... =
~(,,..._ '")\. R f01{1-11t}thduic u
----.
~
(S)
Thus for bright as well as dark rings, we obtain
~
"'
~
(9) ./1,,V.
Since 11• / for air-film,
above equnuon gives
~ ~ 11
~
;,
,-. '
' '
', R
J
1
_,o_,._ ..._o,.
~
(10)
.J mJ.
)
PROCEDURE
)
Level rbe tr:i' clling microscope with its Fit! I 3n
)
' ' ~
2
Adjust the glass plate G, for maximum visibility of the point of contact of lens L with the glass plate G
3.
Move 1h.e microscope to the right of the central dark -spoi (say order 'n', this is because the central ring is often broad and may not necessarily will be zero order) and set it on the extreme visible (say n+20th order) distinct daric ring so shat the cross-wire perpendicular to the direction of movemem of the microscope passes through the dark ring and is tangential to it. Record the microscope position from the horizontal scale along with its number with dark ring around the central dark spot as the f~t dark nng .
4.
Move the microscope to left and record the position of the 16"' dark ring. Continue shifting the microscope to the left and record data at an interval of 4 rings (i.c l2'h, g1h and 4•h ring)
J
1
>
., ~
;)
3
5.
Now move the microscope further to the left so that you cross the central dark spot
and reach the 4"' dark ring on lhe left side of the central spot. Take rbe reading of this . . 4 1h das k nng.
:J ~ 6.
Continue shifl1ng the microscope 10 1he left and rake readings al an interval of four rings rill you reach the 20.., ring.
7.
Now shift tbe microscope to the right by rotating the horizontal knob in the reverse direction. Repeal rbe same process mentioned in steps 4, 5 and 6 till you reach the 2o•h ring in the extreme right side of the central dark spot.
8.
From these measurements, evaluate the diameters of different rings
9.
Now choose any four pairs of rings from your readings and evaluate the difference of square of diameters for these four pairs. From these data you can find out rhe vafue of R for each of these four pairs as given in Table 2. Mean of these four values of R gives you the value of Radius of curvature R of the plane-convex lens.
~ ~
<\](IS ven real Arran~e rhe set-up tis shown in on the air-film. Newton's Rings will be clearly seen.
~
)2
l H~ l• I \ ,\ I I ( 1 ~
~ oble I:
-
~ ~
-
R ""
'· ucd
MSR
VSR
.
in
(0) of rhr rings
cm for rhe .
Total:aM
s.n-v.s
-~
ri!.ht(r) leO(l)
~ ~
ri2ht(r) ll'O(I)
'
rii_ht(r) left(l)
')
riJ11.ht(r)
~
t I...
tr ....
~ r ...
i
1.. ..
l.
r ...
t 1... + l' ...
~I.. ..
TI...
I
Dao meter D
Mean D
R, · R,
an cm
-
x v.c
' I....
right(r) ll'O(l)
--
Right end of the nng(R.) Total-MS V.S.R M.S.R R ... V S.R
RXVC ll'O{t)
~
~,
of the diameter
- Ld\ end of 1hc rim?.CR,)
from
·.,'
minnriou
Reedmu of rhc imcroscope
N
~
D~1('1
+ r ... tJ. ..
tr ....
~I.. ..
+ r ...
tr .... + 1. ...
i I...
~ r ...
tr ....
(l) .... (r) ....
. ...
(1) .... (r) ....
. ...
(l) .... (r) ....
....
(l) .... (r) ....
. ...
Q) .... (r) ....
....
CALCULATIONS Table 2: Determination
Ring
Mean
no.
D U\Cm
01 [cm2}
or R
from the data of Table I
Value
Value of
Value of
of
n
m
n+m
lens is found
R
D~+m -D~
MeanR
4..tm
mcm
mcm
RESULTS The radius of the piano-convex
o•n+m-D'n ~ (cm')
10
13
be R =
p
1'
2
I
l11 I
N!-)
lh
ct up mu
Th
micro
m t ny \'-r:\Y durmg per form th
ope must ahH\)'S be moved m one direcnon 10 avoid
I ns (L) and glass plate (G)
appears '1
not be <.!1sturbcu
the readings, so,
1. km
Th
1
I\ few
AS
in
xper
111)
n1
n pnr11<.:uf:ir
set while
;iny backlash CrTOr bould be set
in
such a wa)' 1ha1 the cenrral
point
dark.
. . nngs near the centre of the pattern should be avoided while rakrng readings.
ERROR CALCULA TlONS
·~
The radius of curvature is calculated from Equation (3). viz
R=
,j
D~+m -D~ 4~m
-~
Since D,. .... and D,. arc only measured, the maximum proportional error in R is given by
;)
2.oD D,,. -D,,
~
1111
~
·~ ")
Now the maximum error in measuring
o,,.,,. or D» is oD = 2 x Y.C.
Hence,
= 4 x Y.C ( aRif?)~·.._ D,,.,., - D,,
")
:3 ~
Now calculate the maximum pcn:cnoag«rror as ( ~)_
X 100%.
~ ~
DISCUSSIONS
~ ~
3
-
~
~ ~ ~ ~ ~ ~
..._
__..
10
____
w_oR_K_IN_STRUCTION
DETERMINATION OF RIGIDITY·MODULUS
BY STATIC METHOD
_l
_.,
WORK INSTRUCTION
[
- -·--·---- --
I 0
NAI\
OF EXPERIM"ENT:RJGIOITY
- --- ----
MODULUS OY STATIC METHOD
Q
OBJECTIVE:TO DETERMINE TIIE MODULUS OF RJGIOITY (17) OF THE MATERIAL OF nIE \VIRE BY STATICAL METHOD .
3.0
PRINCIPLE:Lct the lower end of a wire of length J and radius r be twisted by an angle of 0 radian by the application ofan external couple of moment mgd. Where ~g is the weight
of the mass m placed on each pan and d is the diameter of the fly-wheel. Due to this twist in the wire, an internal couple of magnitude nrrr48/2l will be set up which will balance the external couple. LI---
OQ9';.c:
...A-:...,+
'Pf r4tl tor equiilibri 1 ium"21' = mgd &-.
V
l~
If the~
in the wire be 0° then 0° = ~
H eoee, ipr2r'•' 3601_
= 8 ~ian
. idi1ty11 = -:J:r 360lgd (m) = mgd _or ng1 0 If
'
r
•
\
I 2.
WORK INSTRUCTION 40 4.2 4.3
1001..!>IAPPAllATUS llEQUllU~D: R1g1d1ty modulus setup sloucd w 1ghts Slide Cahpcis
44
Screw Gauge
4.5
Meter Scale
5.0
Procedure:
5.l
5.6
Measure the distanceof the wire from the fixed end A and B of the wire. Measure the diameter of the fly wheel 'd' by slide calipers, Measure the diameter of the experimental wire in various places and al each place reading arc taken in two sections at right angles to each other. Calculate the radius 'r ' from mean diameter. Gently placed slotted weight on the hanger. Wait for few minuses & note down the reading of the twist in pointer P. Increase the load in steps and till the maximum permissible load is reached. Note the readings of the pointer P. Now decrease the load in steps and note the pointer reading. Calculate mean reading.
5.7
A.graph is drawn
4.1
5.2 5.3 5.4 5.5
5.7
with load and twist. The graph is straight line. Calculate ;0 from the graph.
Calculate rigidity modulus from the working formula by putting mcasurcd and ca.Jculated data.
~ ~ ~
II)
"' ~ ~
6.0
EXPERIMENTAL
DAT.A!
6.1
Measurement the length of wire:
~
No. of Observation ~ ~ ~ ~
., ~
~
~
I 2
3
Length of wire (I)
Mean Length (I)
-
'
.: '
..,
WORK INSTRUCTION Measurement of the diameter of [ly-whccl,
(,)
• •,. ,,
.--
\
No of Obs.
-
Reading of the Slide Calipers for measuring the diamclcr
M.S.R
Mean Diameter
Tot.al
V.S.R
1
~ ~
• •... ~
6.3
Determination of the radius of the wire:
No. of Obs.
Read in of theScrew augc for measuring the radius L.S.R
C.S.R
Total
Mean Diameter
Radius 'r'
.,,
·~ ~
,
~
:J ~
Determination of the twist (4'0) of the wire for various load.
6.4
No.
Load on
of
each pan
Obs.
in Kg
Reading of pointer in degree (4'o)
Twist
Degrees Load Increasing
Load Decreasing
Mean
(4'0)
~
'1 ~ ~ ~ ~ ~
·~ ~ ~
..
~
..
~
-: -~
....
••
-
WORK INSTRUCTION
DETERMINATION OF ~
RIGIDITY MODULUS I~ , BY :t ~
~
: DYNAMIC METHOD ~
> ~ ~ ~ ~ ~ ~ ~
• ... ~
r
-
\: ~~/\ !)
':I
C.•1t· \
l
•
• ~
t\,,
l.t. d
\
\)../
-J
-· -
1.0
NAME OF EXPEIUMENT: RIGIDITY MODULUS
2.0
OBJECTIVE: DETERMINATION OF MODULUS OF RlGlDlTY OF Tl IE MATERIAL OF WIRE BY DYNAMICAL METHOD
"'.O
PRINCIPLE: The period (1) with which the bob of a torsion pendulum oscitlates, with its suspension wire as axis is given by '\~ 471! I · ~ ,Sit~ .., I "" < T=2Jt or c= -'- ;.-::-;:---.._ '\.. T1 4. T ~ c::- '}_ "~ 'IV\< v .,,
~
.;a,
. . ~~~ Where I is the moment of inertia of the suspension cylinder about its own axis is given by I = l/ 2 (mass)(radius)2• Here c represent the resting couple exerted by the suspension wire of length I for one radian twist as its free end and rs.given by C= n7t y4 /fl . Where n is-the rigidity of the material of itu(wjre,"while land rare eespectively the length and radius of the suspension wire. Hence, .we may write n~87Cll. / T2 r4 . Calculating I and measuring 1. r &T experimentally, we can find the rigidity n of the by employing the equation.If I, r are put in meters I in ~~-m2 then n wilJ be in N/ mi.
1' ~ ~ ~
:.
y'°'
~ :t1~;; ~
;
2...t.
T
~ ~ ~
0
~,
T'-
4 "'1\ __L_ . '').....
-c) \. ";;
'I .,'"f 'i ~,_,
't -e-
-;.1 ~
-r;:;, ~
" 'J..
~
L (-U"
~~~
y'i
~
l~)
\ \..-
~)
~ ~ ~ (
~ ~
'9 ~
·~.,_ ~3
..
~
.
~
-·4
..•
.
1-
~
0
4.0 4.l 4.2 4.3 4.4 4.5
5.0
TOOLS/APPARATUS REQUIRED: Solid cylinder with unifonn cross section A stand with circular scale Stop watch Screw gauge Meter scale
PROCEDURE: S. l Take the length of the suspension wire from the point of suspension to the point S.2 5.3 S.4 S.5
where the cylinder is attached . Determine the vernier const. of the slide calipers . Measure the diameter of the cylinder by the slide calipers Determine the least count of the screw gauge. Then measure the diameter of the wire. Determine the time period (1)of the torsional oscillation of the cylinder .
.. WORK IN. 'TH
EXPERIMl~NTAL
RESULTS:_
upplicd: I) Mas of the cylinder, M=3208 gm. 2) Length of the suspension wire from the point of suspension lo the point where the cylinder is attached, I = 86.5 cm. Table-1 Vernier constant (v.c.) of the slide calipers __ divisions (say, . m) of the vernier scale= __ divisions (say, n) of the. main scale. Value of 1 smallest main scale division (/,) (cm)
Noof o~tttion.
Vernier constant v.c. = (/1 -11)
Value of I vernier division /2
n =-11 m
(cm)
(cm)
Table-2 r der Diameter o fth ccvm Total reading RQdiN!:S cm) of the D(cm) v.s. m.s. - -
Radius R(cm)
Mean D(cm)
1 2
-Pitch of the screw p cm
Table-3 Least count I.e. of the screw No. of divisions on the circular scale n
a
e Least count=p/n
cm
Table-4 Measurement of the diameter (d=2r) of the wire Mean Total reading Readines 'cm) of the D(cm) D(cm) c.s. m.s.
No of obs.
Radius r (cm)
Iablc-S Determination of the period (TI of torsional oscillation of the cvlinder
No of obs
-
Time for 20 oscillation (t)
Mean time
Period Tin sec
~1
r • J
• OPTJ 'AL FJDRE EXPERIMENT
~ ~
OBJECTJVE
the numerical aperture and the energy lo s related
10 optical
fibre
i) ~
To de1crmme
APPARATUS
Fiber optic analogue transmiuer and receiver ki1s. one and five- meters fibr cords. mhne SM:\ adaptors.
-1. ~ ~
J
Scre-9n
F.O.
~
Cable
,.
........
~
IN
~
s ;,
..,
scale
:, :.J ~
TIIEORY
~
The numerical aperture (Na) of an optical fibre is the amount of light what is collected
~
by it at its end.
.;J
The numericaJ aperture Na= I' sinO
~
For
~
So,
~
In the Fig .. I, Set the light beam from the fibre end fall on the screen = W
~
Na= WI (4L1 + W1)111
air medium
,, = J Na - sin (J
~
Where L is the distance between the end A of the optical fibre and the screen. w is the
:>
diameter of the illuminated circle in the screen .
~
3
... 4t
. ~
1--
Screen
The loss of the optical energy is a function of the length of the optical fibre when one joins two fibres by inline adaptor. In this experiment loss per unit length as well as loss due 10 fibre to fibre joints will be calculated 33
18
lfP,.b the power of rhc hgju cn rgy ntcrin3nn<>pl1,1lf1breoflrn31hl .nrJP!I •II• pt1w1·, output then los due to the fibr m n .urcd as lout0(1'/P0) rn J """8 111 tlH In•,,,,. ''' :1 11111t• opuc: I fibre loss 1 equal to El If A be the total lo due to the adaptor 1hr 101.,1 If>•,., 1, equal 10 L t A· If Poi and Pin are the power losses due to fibre" of l<:nB•h-. I , onrl J 1 nnrl J>0, 1« thnt due 10 the combination when the fibres MC jorncd with on mlt1w. '_,MA 'l conmbuuon, then 1hc loss due 10 the fibre of one metre length and rhe SMA 1.,. uvcn h~
•
• • • •>
the
Pol: P02 And similarly loss due 10 the fibre of length 5 metre and the SMA is given by
>
• ~
Therefore, loss per unit length, € = (Po2 - Poi) I (Lr L1) dB/m And the loss due the inline SMA (fibre-to-fibre-joint) is given by A= (POJ - Poz) - €La dB/m
~
PROCEDURE
~
I.
~ ~ ~ ~
To connect the J metre optical fibre with LED part of the transmitter kit so that light seen to pass through the other end. To make the room dark. Then 10 insert tbe orber end of the fibre through the hole of the L-shaped numerical aperture measuring kit. To place the circularly calibrated screen plate vertically on the marked end of the L-kit. To switch on machine. To make one circle completely bright on the vertical plate by adjusting the intensity knob. To note down the distance L. To measure the value of 1he diameter of tbe circle (W)
rs
~ ~
2. To move the vertical circularly calibrated screen at different positions and note down diameter (W) of the completely illuminated circle in each case.
~ ~ ~ ~
, "
3. To take out the output end of the fibre from the L-kit and to connect it 10 the power measuring poll of the receiver kit. To apply an input voltage by Turing the set Po knob. To make sure 1ha1 the fibre is fully stretched without any coiling or bending. Now, 10 measure the input voltage and the out put power with the help of Muhemeter. This loss is Poi.
~
~
4
To repeat 'Step 3. For the 5 metre fibre. The input voltage should be same as earlier. This power l()ss is Po2-
5.
To repeal step 3 once again by joining two fibres by inline SMA. This power loss is Po;.
~
, • ~
~
I~
l~
34
t
T:-iblc I: Octcrmin:-ition
s
I
NO
--
of numerical aperture Mean Na
Na= WI (4L" + W2}tn
W(mm)
L(mm}
I I
I I
I .
. r-
Table 2: Calculation of loss of power ~ I
3
SI.No.
Po1
P02
€
= (Po2 - Po1} I
Pol
(L2- L1)
~
.
ao
a,
3
33
as
Ao
A,
I
I I
3 ~ ~ ~ ~ ~
RESULTS
~ ~
"3 DJSCUSSJONS ~
-
~
~
..,
~
~
.I
A= (Pol - Po2) - €L1 dB/m
~
35
A3
As
I,
l
~
AREY-FOSTER'
IlRJDGE £XP£RJJ\t1ENT
OBJECTJVE
~
To determine rhc resistance per unit length of determine the value of an unknown lo.w resistance.
~
APPARATUS
~
Carey Fosler bridge, galvanometer, two equal resistances (sa¥ I
~ ~
.) ~
• ~
~
fl
C<>rcy-Fosrers
n.
bridge wife and hence
each), voltage source (2v
power supply). connecting wires etc.
THEORY The Carey Foster bridge is an electrical circuit that can be used lo measure very low resistances. It works on the same principle as Wheatstone's bridge, which consists of four resistances R1: R2, R3 and R4 that are connected to each other as shown in the circuit diagram in Fig. l. In this circuit, E is a voltage source, G is a galvanometer and K1 and K2 are two keys. "If the values of the resistances arc so adjusted thar no current flows through the galvanometer (balance condition), then the resistances R,, Ri. R3 and ~ satisfy the relationship
, ~
-~ ~
(I)
In a meter bridge, two of the resistors, say R3 and R•• are replaced by a resistance wire of one meter length and uniform cross sectional area fixed on a meter scale. Point D is a sliding contact thar can be moved along the wire, thus varying the magnitudes of R3 and R4• The Carey Foster bridge is a modified form of the merer bride in which the effective length of the wire is considerably increased by connecting a resistance in series with each end of the wire This increases accuracy of tbe bridge.
ic1--~1l1lt..
E
I
Fig. J Whearstone bridge
....
l !' ') 1 \ ·.
•
•
·d r
• t
-l
-
•
•
..
t
.JI J l
1
-----
l
F\3.2: Ccarey Fo t r t>r1d8 ctreult dl.-cmm 11.e circuil die m for \he Corey os'cr brtdgc is 1hown in Pia. 2. Two otond&rd low resi~'anocs, P nd Q, of 18)' I ohm e h Ott COtmeClcd in the inner gap 2 nd ), A known ~. i.e., &a tional resisumcc box X ond lhe unknown tcrnce Y who e r. I 1 nee i to be detcmuncd re eonneeted in the outer 8ftP' 1 1md A. s; pc tively. A one met.er kme resislance win or uniform orea or cross section is soldered to the end of rwe copper triP'. Since tbe wire hos uniform eross-secrien I Mea, 'he res· tonee per unit length i the me along the wire. A golvop9~cr Q l$~Q.D.Ot ~ii. ~l "o~l B.M
The four points A, B, C ond .D in Fig. 2 exactly correspond to the imilarly labeled points in the Wheatstone's bridge circuit in Fig. I. Therefore irthe balance point i located at a distance /1 &om£, then we gel P -
Q
D
X+o+l,p Y+P+(I00-1,)p
(2)
where p is the resistance per un,it lcng1h or the wire, and a and /3 ore the resistanca due to eod corrections at the left and right ends. If now the positioM of X and Y ftf'¢ interchanged nod the balance point is found at a distance /2 from£, then ·
P
y +a +l1P
(3)
-= Q X +P+(I00-1,)p ,;
~
From Eq. (2) ond (J). we ob1airi X +er + l,p Y+{J+(I00-1,)p
• __ Y_•_a_+...1/1=.:.P __ X+IJ+(IOO-l1)p
2
(4)
2.?
..Y
••
I
>'
- f)
I -(10()
I (1
I
•, •
I
~
I 00
,.
I,)
y
I
y
J), (100
>'
i
I
I ('f
I
fl
I
IOOp
J) .. ( I 00 I,) p
(S)
fJ t>(IOO-/))p
1,)p=Y'
Or )' = X - (11
-
I, )p
(6)
~
Thus once we know II • I 1 • p and X• the unknown resistance Y can be determined using Eq, ~
•
(6) In order lo deterrmne
x
p=-/2 -1,
~
.a
(7)
p can be determined by short circuiting Yaod measuring I, and I,.
Thus ~
p , put Y = 0 in Eq. (6) 10 gel,
PROCEDURE
I.
~
~-
I.
To find the resistance per unit length of the wire ( p)
Make the circuit connections as shown in Fig. 2. Make sure rha1 all connections
are
ligb1.
~ ~
2.
Connect the given resistances P arid Q (JO each) in gaps 2 and 3. Jn tbis pan, Xis a fractional resistance box and Y is a short circuit (zero resistance).
~
3.
Switch on power voltage source so that current flows through tbe circuit.
~
4.
Firsr set rbe resistance X at zero and see if the galvanometer shows opposite deflections when the jockey is pressed al the two ends of the wire. Also check whether the nu JI point is localed around the middle of the bridge wire. J fit is so, then the connections are likely to be correct.
5.
Now
6.
Locate the balance point. Record the distance of the balance point from the left end (point E) of the wire as Jengch ".
7.
Reverse rbe direction of current flow by tbe commutator and again record the balance point I, for 1hc reverse current. Take average of 1, for direct and reverse current (see Table l) in order 10 eliminate l~e effect of any thermo emf
~
,
~
-~
•
, ,• ~
~
sci
a small resistance in X, say X
= 0. IQ
8.
Increase resistance X, in steps of say 0.2 Q. 0.4 Q. etc and repeat steps 6- 7 each lime.
9
Interchange rhe posiuons of X and the zero resistance Y and repeal steps 6- 7 for rhe same set of resistance values for X The corsesponding balance point disrance
~
a
,• ~
3
r ~·
, s
urcd tr m th
Ill
>
'· blc
.,
I I.
~
sam
end of th
To find an unknown
bridPc w1r<' should be record d
low rcsislnnce
~
2
I
•n •h
d;;I;\
Y
Remove the short c1rc1111 and set the resistance resis.tnnce.
~
:i~
Y
al a
small
value
unknown
as
R~peat the cm ire sequence of sieps :>-9 in pan J of the procedure and Jill up Table 2
3 OBSERVATIONS
3
Table 1: Determination of the Carey Foster bridge wire (with Y
~
I
~
SI
x
No.
(0)
Position of balance point with Y (= 0) in the Right gap ( /1 ) Left gap ( 11)
~
Direct
~
current
(cm) Reverse Mean current I,
11• I, (cm)
= 0) p=
x /2 - /I
(cm) Direct current
Reverse
Mean
current
(O/cm)
t,
3 ~
3
,
~
~ Table 2: Determination
~ ~
SI No.
X
of the unknown low resistance, Y
Position of balance point with Y (- 0) in the
/l - '1
( O ) ~--R-ig_h_t_g_a_p_( /-,.-)---.~--L-eft-'--g-ap_(_/_ (cm) 1·-)---i
~ (cm)
(cm) (0)
~
Direct
~
current
Reverse current
Mean
/'
Direct current
I
Reverse current
Mean
1i ·
~ ~ ~ ~
! ~--+---+.--4----+--i-----4---+---t--t------1
~ ~ ~ ~
I
4
l•
E-=-==--:r~---~---+---__.__-+--F---+--_-r!---~-~= 4
2 '-1
CALCULI\ TJONS
. r~
•, > • ~
~
1 C:tkulotc the value of ( /1
for each value of X
- /1)
in
Table I
2 C
in Table I using Eq. (7). ~ Calcutare the meanp from the values obtained in Table I for differcm X. 4. Usmg this mean value of p in Eq. (6), calculate the unknown r~israncc Y for each row mTable 2. 5. Use rbese results 10 calculate the mean value of Y.
RESULTS
=
Resistance per unit length of bridge wire, p Value of the unknown low resistance, Y"" ERROR ANALYSJS
~
p=-
~
op) a(I -l) 2a1 ( _p max = 112- I, = -11 - I, 1
~
x 1, -/1
.
(Assum~ng the face value of X to be correct)
3 Where ~ ~
, ~
I
_)
ol
= 1 smallest div. of the meter scale
Using a typical observed value of ( 11 -I,). we cakulate the maximum percentage error in p
as
( ap) P
x 100%.
max
~
Y
oY.....
~ ~
=
>
.,
= ( 1,·
-
=X
-(11 -1,)p
t; )op+ p.20/ ( Assuming ax
p[(i, -1,) ~ + 201]
= P['' -1,· + i]2a1 ( ar) Y "'" R 1 -I,
~
2
Now using a typical set of observed data. we can calculate
~ ~
DlSCUSSJONS
~ ~ ~ ~
4 ......
=0J
s
(a;) ...~.
X100%
, ,.•
l.1\Sl·.I~
••• • •
Vl~ fhfl1,
Io
c1 'IC1 min
p uem w uh
llOO
J\PPARA }US L1\SER
I\
l)IFFRJ\ "'TlON EX~EJ~IMEN'I
the wavelength
of n given LASl:R
source by (ornung
plane imnsrmssrou gra1mg
d1\)(JC
module with power supply, Spectrometer, Gr:l~i.ng,
L1\SER derccior
~
~
• • •.
THEORY The LASER Diode module and LASER detector are mounted in place of collimator and telescope of a spectrometer respectively. The grating is mounted on prism base of the spectrometer. The emitted Laser beam is diffracted by grating. The diffraction pattern can
I
, ,, • • • ~
be seen on a screen by holding i1 at the place of detector. Here one can notice the decrease in the intensity of light as one move away from the zeroth order towards the higher orders.
Now the wavelength of the LASER light is obtained from the relation
A.= dsinB m Where. d is the pitch of the grating m ts the order of the maxima
8 is the angle of deviation ~
.
~
~ ~
• 9 ~
(nboot Im)
---Fig:J
~ ~ ~
41 ~
;, ~
10
.J'I Opoca ....
·
baneb
PR_~ DURE Switch on the LASER source
• •a
ei the spcctronx1cr as 11 source and detector should be colhncar
At thrs position t:ike rhc: darn ofrhe both vermcr scales (vernier I&.
.
vcnucr
II)
Fhrs
is called direct readinss eNow place the grnting ar rhe centre of the prism table
s
Laser beam is now diffracted-by the graring and .make a spectrum like fig I
6.
Keeping undisturbed the arrangement, now take the darn of rhe both vernier scales
~ ~
for central order i.e. O'" order. This readings should coincide with rbe direct readings.
• • •.
7
Now move the LASER detector towards left from the central order and set the detector at the left -side I" order. Note down the data of the both vernier scales in Table I
8. After taking the data of the Isa order again move the LASER detector rowards left and sci the detector at the left side 2nd order. Note down the data of the both vernier
~
scales in Table I
~
9.
• •
foUow the same procedures for rhe left side 3'd order.
I 0. Now move the detector
10
the opposite direction and get back
10
the centra I order
Check the readings again and ensure that should matched wirh previous central order
,•
readings . I I. Move the detector towards right from the central order and repeat steps 7, 8 and 9 for right side lsi, 2nd and 3'11 oder.
~
12. Now calculate the wavelength of the LASER source for 151, 2"" and J'J oder in Table
~
2 by using the data of the Table I
~ ~
OBSERVATJONS
~ ~
•
d=
Vernier consram of the spectrometer =
~ ~ ~ ~
41 ~
4 ~~
f 'J
•. •
• • .•
Tnbte t
.
~ n
~
0
I
ol llljl\
i
OHi
~
>
• • •a ,
or n1\~l1'
1111'111r1H
L ff
order
order \'frnitr
--
II
VSR
Toc:1I
MS
VSR
lo1:tl
I<
(dcgr
R
(clt'gr
(dt81
(}'I
~)
o:
(dtg1
(dcgr
C<')
ee)
M.S. R
V.S.R
Toc:il
~s
V.S.K
(dcgr
R
(d
(deg1
(dcg1
ee)
B," . (degr
(degr
C'C)
ee)
ee)
1
ee)
---V('rn1cr- II- --
Vernier I
i\1 S
ee)
of d vinrion
LRiljhl
Vernier I
01t1f't
.
l\·h'.,
cc)
rotl'\I
gr
O"I (deg1
ee)
ee)
0(,~111 :ii)
I
2
~
>
•
I
3
~
~
3
CALCULATIONS
~
~
Table 2 : Measurement of wavelength of the source Order
or
maxima
. 281
= ()~ -B,·
(degree)
281 =Bi -02•
28
= 28, + 291 2
(degree)
(degree)
. '
~
~
RESULTS The wavelength of the LASER source is found lo be ..1. =
20
9(degrcc)
..1. (cm)
ERROR t\NALYSJS
) = r!_~in
• '*• ~
111
Hence,
•. ,,• • ~
•
~
>
•. •
~
a ~
( a;..) ).
Where
ae
=2X
V.
DJSCUSSJONS
= cotB.ae 11\.1\
C. of spectrometer
Now ca ku late the maximum percentage error as [ ~
~
•· •
e
?t] max X 100 % .
• • •• • • ,. • • •.» •.a
n
J•
llVI•
APl'/\Hi\1
ti.
10111,•ur\th ·,
D1p1•1v
.
Pow1·1or11
'' m 1 t, p11.111, •p11111
v •I,
m.111.1lof
o
p11·1m
our e 1rnd hydrogen di.
hnre
h.1
·1 Jll~ORY
'9
(.\) = 1-'Fµ0-1-flc
(l)
Where J.tr and uc Are refracrive indices of F. lines bluish green 4861 A) Md C- lines (and 65'63 A) of Hydrogen spectrum and µ0 is the refractive index for D- lines (5893 A) of Sodium (Na) respectively. The refractive index. ).tf. ~ and µ0 of the material of the prism for the different lines can be obtained from the formula,
~
am
Where, A and arc the angle of the prism and the t1nglc of the minimum deviation respectively for the
~
line concerned.
~ ~
3 ~
•
• ~
,
> ~ ~
~.
DIAGRAM
OF SPECTROMETER USING PRISM FOR STUDYING DISPERSIVE PO\VER
~ ~ ~
l6
DIAGRAM
0 I A C RAM
FO.R ME/\SU.RING
F 0 R i\l
r AS UR
l7
ING
t\
1\NGLE
NG I 1- 0
r
OF
PRISM
0 EV I A l 10 N
!-
•.. •
•
PR(
• •• •a
1) 11)
Fnlm F. Al
r.r ... 1 the level mg. adjusuneurs and focu 111g of the spectrometer bas 10 be derermrncd
Nc:(t tbe angle of the prism(/\) to be set on the prism-table
in
have lob
done
To do thrs. the prrsn; has
such a way that us vertex points
toward
the
collimator and 11s rcfracung faces (AB and AC) gel almost equally the parnllc! rays coming out of the collimator
{ Fig. I } The angle between the rays re fleeted
from these two faces will be 2A if t.he prism angle be ·A. This is because when the face AC turns and goes to the position of AB, then the angle through which
~
the reflected rays turns, will be equal to 2A. Hence, if the angle between the rays reflected from these two refracting faces is determined by the spectrometer, then
->
• • ., ~
the value of A will be obtained . iii)
The vernier-constants of both the circular scales are determined and noted .
1v)
The prism is properly set on the prism-table {Fig 2) and the sli: is properly illuminated by a sodium vapor lamp or a burner .
v)
.I
The telescope is rotated gradually and the image of the slit reflected from the face AB of the prism,~ received in it in the position T1. The cross-wire is set at a particular end of the slit-image and the reading of the telescope is noted from
>
the circular and the vernier scales. The reading are taken thrice and the mean is taken. Let it be M1.
~ vi)
~ ~
The telescope is then rotated to the position T2 and similarly slit-image is received init when light is reflected from the side AC of the prism. Readings of the telescope arc taken thrice as before and the mean reading is noted. Lei it be Mi the angle of the prism (A) will be give by
~
.a
•a .a
vii)
To determine
A= (M,-M~)/2 the angle of minimum deviation(l>m). the prism is placed on the
prism-table in such a way that one of the faces ( AC) points towards the collimator ( Fig 2).ln this position, rays coming out of the collimator will be refracted through the face AC and will be finally come out of the face AB. If the
~
prism table rs gradually rotated and the slit-image is viewed through the telescope, it will be found that the image is deviated up to a certain point and then comes back in the same direction, irrespective of the direction of the rotation of the prism-table. The point whercfrom the image returns back, is the position of minimum deviation. Keeping the prism at the position of the minimum deviation. the slit-image there is focused in the telescope tn rhe position Trannd rbe telescope reading is taken. This reading is taken at least
~
lhnce and their mean (R1) is taken
, ~
~
~ ~
•
~
28
''
111)
Ih
fll l\Jll
•• • a ,,
,,
• • ,. ,
th
II
WHhd
I
I
' I
r
I;()
I lei c deicrmining the values of 1\ and[>," •he value of the refractive index (11) of1hc motcri31 ~fthc prism can be determined ·
x)
Now the sodium ligh: is replaced by hydrogen discharge lube which rs excited by means of an induction coil or n transformer. The tube is held vertically and the slit is illuminated by ii directly. On viewing through the telescope with the prism set properly, well defined lines of hydrogen spectrum are visibJe. The strong C-li.nc in the red is identified and ii is focused on the cross-wire al the minimum deviation position of the prism. Telescope readings tire noted. Sim~arly, the strong F-line in 1hc bluish-green is identified and focused at the minimum deviation position of the prism.
xi)
Finally, the diJ"Ccl reading of the slit-image is taken from which the values of rbe minimum deviation (6,,., corresponding to the red, bluish-green and yeJJow lines are obtained.
~
~
>
•, , •
,.,
• tnble nnd the tcle<:cop ·~ bfou3l11 ro rh I t 1 l111a r.' 0,"111~" t '•0111O11ih1nrn1or can nl r the telescope drr ct ly fire 0111 focus d' 11h lh mn side of the sht-imagc a be for nnd the ' .l( I ino 0 lhe I le · Op ·~ noted 1 h1 1 known As rhc duecr re:iding Th I d11 01 IOk 11 If • lr e and the menn reading (R2) is determined. Thus rhc nrteor . . . ' mullfnum dcv1otion H>rn) of the prism will be S,,. • (R1-R1) 111
xii)
•
Substituting the values of 6,,. for the different Hoes in equation 2, the values of µF, llc µoare determined, from which the value of the dispersive power (a>) of tbe material of the prism is obtained using equation I
~
~
OBSERY A TlONS Vernier constants of the spectrometer i) Vernier constants of rhe prism-table Vernier:=
~
ii) Vernier constants of the telescope Vernier:
=
~
,• ~ ~ ~ ~ ~
4'
29
\ ~~
.
,-1
• •.
'
..
Tnbtc l : Detcr miurn io n of :lnglc (A) of the pr
••• • •.
i\'I a i .n Seal e
:.>
·-c
C>
>
Vernie r
.
II
lle:H.lings for second image a1 T1 Mean ~ ,\ ):li Vernie Tota Me:l (M,) n n r I Seal (M2)
Readings for first image
T,
:\I
I
Tot al
i.111
I
•
Differcuc c of the mean readings for rhe
\•lean I he
of
diffrrc
nee (2,.\)
hVO
e
(i\'J, IVJ,)
->
• • • •> •
First
...
...
...
...
...
...
. ..
. ..
. ..
...
. ..
.. .
. ..
. ..
I Seeon cl
. ..
...
...
...
I
...
Table 2 : Determination of angle of minimum deviation (o,,.)
~
· J. For Sodium Jigbt
• •
Readings for minimum
~
~
Readings for direct rays Mai n
Vernie r
Seal ~
• ~
e
Total
Mea
{R2)
n
AngJeof the minimum deviation (bm
=R2-R1)
Mean "~lue ] of the Angle of the · minimum
I I
deviation {5,.)
I
Firsr
~
Se-con cl
I 30
,
CA'
'11. For C-Hnes C rtd) of Hxdrogcn $pcctrnm
-
f
R~:)ding for minimum deviation Mnin Ver nie r ~ Tora Mc:in Stale I (R,)
.... 61 e
....u
>
r
nc:idings for c.Jirect roys Main . Vernie Scale r
Total (R2)
J\Tean
Angle of the minimum deviation {om
-R2-R1)
.
. First
...
... . ...
. ..
...
...
...
. ..
...
... :
. ..
Second
'm.
if --
<> c
. ..
...
...
...
...
...
...
Mean
Angle of the minimum deviation (Om =R2-R1)
...
Re:idings for minimum deviation
Readings for direct rays
Main Scale
Vernier
Tolal
Mean (R,)
Main Scale
Vernier
Fint
...
. ..
...
...
...
. ..
. ..
. ..
. ..
.. .
...
...
...
. ..
. ..
. ..
. ..
. ..
:>
Total (R2)
~ ~ ~ ~
...
For F-lines (bluish-green) of Hvdrogen spectrum
<>
I..
ivJt>an v1>J11r of 1he 1\nglt of1hc rnlnlrnu m t.lc\'l~lion (5rn)
Mean value of the Angle of the minimum deviation (5m)
~ ~ I ~Second
' -~
31
...
.
i ·--··
1\l.
lJl~1\flON
Usmg cquotJon (2) rhc rcfmcuv uidrccs '''· Pr rand Jin of J· llnd -1111 · of If ydio ''" Sodn1m D hncs are re pecnvcly found out from rhe values of co1rcspond111 ~ ·"'~' mmunum dcvia1ioo (~ ... ) ob1oincd. Then subs1i1u1ing (I) the value oft~ dispersive power of the material
the value
of 1•r 1•r and 1•0
r1CI
11
'•
of
·q1rn11011
111 1
of 1h~ prism is determined
PRECAUTIONS i)
In all
cases of focusing. the rmmrnurn
corresponding· there. ii)
iii)
,a
10
each line has
10
de vint ion
position of the
pri:'m
be ascertained and the telescope rnusr be set
Sc"Cral independent settings of the cross-wire are 10 be made for each reading avc»ding thereby any position errors in laking re.-.ding.s of the vernier. The discharge tube should be held vertically in front of the slir properly, so lhar the brighlest pan of the illumination remains in fronr of rhc slit
ERROR CALC1JLA TIONS
Hcnee , maximum percentage error in w iJw
w
6µF+Oµc µF-µc
+
oµo µo-1
This is true when tbe errors in #lF. µc and µo are approximately equal and ID is small.
DISCUSSIONS
32
r, I
, ~
J J
M~. !-.U• rr11c111 o: l'h rrnnl Co11cl11 ri 11y l>y l,c·(·',
111rlllod
Aim
T ckte1 mine thermal Lee 's rn thod Re'qu] ires:
conductivity
of a bad condu tor (glase) 111 forrn of :1 disc
"""'i~
·
~
>
•a
.. ~
.»
> > >
,
. ~
• • • •
9 ~ ~
• •
9 9 ~
...•
( l) Lee's apparatus and the experimental specimen in the form of a disc
(2) Two thcnnometcrs, (3) Stop watch, (4) Weighing balance, (5) Special lamp stand (6) Boiler and (7) Heater Theory:
Thermal conductivity, k, is the property of a material that indicates its ability to conduct heal Conduction will take place if there exists a temperature gradient in a solid (or stauonary fluid) medium. Energy is transferred from more energetic to less energetic molecules when neighboring molecules collide. Conductive heat flow occurs in direction of the decreasing temperature because higher temperature is associated with higher molecular energy. Fourier's Law expresses conductive heat transfer as (I) where H is the -steady state rate of heat transfer, k is the thermaJ conductivity of the sample, A is the cross sectional area and (T 2 - T1) is the temperature difference across the sample thickness 'x • (see Fig. I). assuming that the heat loss from the sides of the sample is negligible, To keep the loss from the-sides small. the sample is H = kA (Tz - Ti) made in form of a thin disk with a Jar,ge x cross sectional 31e3 compared to the area exposed at the edge. Keeping 'A' large and 'x ' small produces a large rate of energy transfer across the sample. Keeping x small Fig. J also means that the apparatus reaches a steady state(when temperature T1 and T2 are constant) more quickly . Generally speaking, there are a number of possibilities to measure thermal condocnvnv, each of them being suitable for a limited range of materials, depending on the thermal properties and the medium temperalure. The most commonly used methods are Searles method and Lee's disc method, for good and bad conductors of heat, respectively. In the experiment, we will use Lee's disc method to determine the thermal conductivity of a bad conductor, e.g Glass
l
. " " • ".
3
~
.
,
~
• •
De o 1ption
of I cc'
apparatus:
TI1 opparatu
hown in Fig 2 con ists of two pails The lower part C rs circular metal disc. The expcnmcntal specimen G, usually rubber, glass or ebonitc (here 11 is glass) is plac don it The diameter of G is equal to that of C and thickness is uniform throughout A steam chamber 1 placed on C The lower part of the steam chamber, 13 is made of a thick metal plate of the arne ~1amcter as of C The upper part is a hollow chamber in which two side tubes are provided for inflow and outflow of steam. Two thermometers T1 and T2 are inserted into two hotesin C and B, respectively. There are three hooks attached to C. The complete setup is suspended from a clamp stand by attaching threads to these hooks.
Steam in Steam Chest
-+
Steam Out
~
.a
,
Tz
Brass Base B
T,
Brass Disk C
-Glass disc (G)
-:.:I
~
, , ,
~
J_ x
Fig.2
~
~ ~ ~
•a ~ ~ ~
Photograph of thermal conductivity measurement setup
~
,
~
~
;, ~
2
,, ..
, •
Wl~n steam no~ This
IS
th
ready
for omc tune, the temperatures recorded (T1a:id11)
~
Let at the steady state, temperature of C
~
Temperature of 0
~
Surface area of G
3
Conductivity
~
Thickness of G = x
••
• ~ ~
'
= T1•
= T2.
=A of G = k
H=
4T
ms-ctc
.......
~
>
• • • • • ~
~
~
a a ~ ~ ~
k
(2)
Equating ( 1) and (2) and simplifying. k can be determined as,
9 ~
'"'"'Y
Hence amount of heat flowing through G per second. H is given by Eq. (I}. When the apparatus is in steady state (temperatures- T1 and T2 constant}. the rate of heat conduction into the brass disc C is equal to the rate of heat loss from the bottom of it, The rate of heat loss can be determined by measuring how fast the disc C cools at the previous (steady state) temperature T, (with the top of the brass disk covered with insulation). If the mass .and specific heat of the lower disc arc m and s, respectively and the rate of cooling at T1 is dT/dt then the amount of heat radiated per second is, ·
t
.a
radually remain
Si3lC
.........
(3)
Procedure:
J. Fill the boiler with water to nearly half and heat it to produce steam 2. In the mean time. take weight of C by a weighing balance. Note its specific heat from a constant table. Measure the diameter of the specimen by a scale or slide calipers, if possible. Calculate the surface ~ A=n 3. Measure the thickness of the specimen by screw-gauge. Take observations at 5 spots and take the mean value . 4. Put the specimen. steam chamber etc. in position and suspend it from the clamp stand. Insert the thermometer. Check if both of them are displaying readings at room temperature. If not, note the difference 0, is to be added to (T2 - T1) later . 5 Now stem is ready. Connect the boiler outlet with the inlet of the steam chamber by a rubber tube . 6. Temperatures recorded in the thermometers will show a rise and finally will be steady at T1 and T2. 7. Wait for 1-0 minutes and note the steady temperature. Stop the inflow of steam. 8 Remove the steam chamber and the specimen G. C is still suspended Heat C directly by the steam chamber till its temperature is about T, + 7°.
r.
3
•
•
9
R move the steam chamber and wan for 2 - 3 minutes so that heat is uniformly distributed over the disc C l 0 Place the insulating material on C. Start recording the temperature at Y1 mi nut~ intervals. Continue ttll tbe temperature falls by 10° from T1•
Observations:
ti)
Details of the sample G (a) Diameter: (using scale/slide calipers)
Table-I: SI No.
Diameter (cm}
Mean Diameter (cm)
I
2 ....
~
~
Surface area ofG =A=
~
Thickness:
a
Pitch= SI No.
Initial (£m)
!~
,~ 1• ,~
(using screw-gauge)
Table- 2:
~ ~
.
. Reading
Least count= ••••••••••••••••....•••••.••.• I
Final Reading F (cm)
.)
1>
I
1•
la
5
1-s I~
l~
(11)
Details of the lower disc C Mass of the disc. m =
.
~· 4
~
Difference (I - F) in cm
Mean (cm)
•• .• • ••
(Ill)
.. ~
(IV)
~
Specific heat of the material, s= 380 J/kg °C Correction of Thermometers Room temperature recorded T2 ;; ••••..••.•..•••.•. Room temperature recorded T 1 = So correction of thermometers 0 = T2 -.T 1 Steady Temperature Temperature of~= : . .. . .. . . Temperature of B = . Taking thermometer error in to account, the difference= (T2-T,+0)
~
• •• • • • •> ~
(V)
I
Time (minute)
Tab!e-3: Time - Temperature record during cooling
I
O
Graph:
»
Using the data from Table - 3. plot the cooling cwve (time versus temperature) and determine the slope dT/dt = llT/6t at the s&eady temperature T1 (Fig. 3).
~
Calculation:
Temperature (Celsius)
oT
k::: ............•...
~ ~
Discussion and conclusion:
a
ot Time (Seconds)
~
•
9 ~
Probable errors and precautions:
Fig. 3
Don't record T1 and T2 unless they have remained steady for at least 10 minutes. 2. The tangent to the cooling curve should be done very carefully. An error in dT/dt will result in a wrong result fork. I.
~
,~._ ·~.!L 1 •·
s
I ..
-
