Lab Experiments 49
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Experiment-397
S
DIGITISING MEASUREMENT OF
NEWTON’S RINGS:
DETERMINATION OF WAVELENGTHS
OF LED LIGHTS
Jeethendra Kumar P K, Ajeya PadmaJeeth and Santhosh K
KamalJeeth Instrumentation & Service Unit, No-610, Tata Nagar, Bengaluru-560 092, INDIA
Email:[email protected]
Abstract
Using a digital camera and Newton’s rings microscope, software is developed to
determine radius of various Newton’s rings. The camera is attached directly to the
Newton’s rings microscope replacing the eye piece and measurements are made
by the system.
Introduction
Generation of Newton’s rings is one of the most fundamental and classic experiments in
physics. Newton’s rings are formed using monochromatic source of light (e.g. a sodium
vapour lamp) or LED light. We have already published three experiments based on Newton’s
rings [1, 2, 3] which involve determination of wavelength, radius of curvature and energy gap
(measured by the optical method) and coherence length of LED light. In these experiments
we have used the same instruments. In the current experiment, in addition to the Newton’s
rings set-up, we have used a digital camera and associated software to estimate the diameter
and radius of various rings. The digital camera produces photographs of the Newton’s rings
on the computer monitor and the software is used to determine the diameter of various rings.
Diameter of n =1-20 rings can be determined easily in a few minutes time as the software
computes the radius of rings automatically. Hence measurement of Newton’s rings is now
digitized.
The radius of the nth Newton’s rings is given by [4]
ଵ
…1
ଵ
…2
rn =ටቀ݊ + ቁ ߣܴ
ଶ
rn2 = ቀ݊ + ଶቁ ߣܴ
where
rn is the radius of nth ring,
λ is the wavelength of the monochromatic light used,
R is the radius of curvature of the lens used, and
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n = 1, 2… is the number of rings.
ଵ
A graph of rn2 on the Y-axis and ቀ݊ + ଶቁ on the X-axis is found to be a straight with slope
equal to λR. One can determine the slope, knowing any one of the two unknowns. In this
experiment we have first used the sodium light of known wavelength (589.3nm) and
determined the value of R. Then using the known value of R, Newton’s rings are formed with
LED lights and the wavelengths of the various LED sources are determined.
Apparatus used
Newton’s rings microscope, sodium vapour lamp set, solid state lamp, digital camera and the
associated software
Figure-1: Digital eye-piece camera used in the experiment
Figure-2: Newton’s rings microscope fitted with the digital eye-piece camera
The digital eye-piece camera used in the experiment is shown in Figure-1. Figure-2 shows
the complete experimental set-up.
Installing the software in the computer and capturing the picture
The CD containing Newton’s rings software is installed in PC. The Newton’s rings
microscope is placed in front of sodium vapour lamp and Newton’s rings are observed
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through the eye piece. Now the eye-piece is removed and digital eye-piece camera is inserted
in its place and camera is connected to the computer.
To view the pictures go to my computer and view USB video device the following screen
will appear as shown in Figure-3.
Figure-3: Capturing picture from the camera
If there is any picture taken already, you may delete it by selecting it and pressing delete
button. Take new picture by clicking “Take a new picture on the window” as shown in
Figure-3. You may take few pictures of the rings after suitable focusing in the microscope.
Experimental procedure
Part-A: Generation of Newton’s rings employing sodium light and determination of R
Part-B: Generation of Newton’s rings employing a solid state lamp and determination of
wavelength of LED light
Part-A: Generation of Newton’s rings employing sodium light and
determination of R
Figure-4: Newton’s rings observed using sodium light
1. Preliminary adjustments of the Newton’s rings microscope are done and it is placed in
front of the sodium vapour light source [1]. Newton’s rings are observed in the field
of view of the microscope as shown in Figure-4.
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2. The vertical cross wire is brought exactly to the centre of central dark ring and the eye
piece is now removed and replaced by a digital camera, as shown in Figure-2.
3. The camera is connected to the computer and the camera software is opened by
double clicking on the icon. The name of student is entered in the space provided on
top of the picture screen as shown in Figure-5.
Figure-5: Newton’s rings window showing tabular column and student’s name
Figure-6: Window after pressing load images button showing options to load
picture
4. The picture window contains a Table on the left hand side and menu buttons at the
bottom. The following menus appear on the screen:
Capture Image Load Image Clear image Set-Origin Print Exit
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5. Load image button is pressed and new window shown in Figure-6 appears with
loading options. Go to my computer and select USB video device and selected the
image you have already captured. The following window will appear with selected
picture as shown in Figure-7.
Figure-7: Newton’s rings captured by the camera
6. The mouse is pointed exactly to the centre of central dark ring, and “Set- origin”
button is pressed. The X-Y axes appear as shown in Figure-8.
Figure-8: Setting X-Y coordinates axes at the center of the dark ring
7. To find the diameter of n=1 ring, the first row (Ring No-1) in the Table on left hand
side is clicked and the selection appears in blue colour.
8. The mouse is now placed on the first dark ring on the left on the green X-axis and
clicked. A white coloured vertical line appears on the first dark ring parallel to Y-axis.
The mouse is now moved to right side of the first ring and clicked. Another white
coloured vertical line appears on the screen as shown in Figure-9 (a) and 9 (b).
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Figure-9: (a) Vertical line on n=1 ring on the left (b) vertical line on n=1 ring on the
right side of the ring
9. The distance between these two white lines is the diameter of the first ring which is
recorded automatically in the Table on the picture screen.
Radius of n=1 ring = r1 = 845.24µm which gives r12 = 0.714x10 -6
10. To find the diameter of the second (n=2) ring, ring 2 in the Table is clicked and the
cursor is now pointed on to the second ring and clicked first on the left and then on
the right of the ring. This selects the n=2 rings and its diameter is recorded in Table
on the picture.
11. This procedure is repeated for all the 10 rings one by one. In each case the diameter of
various rings is recorded in Table and the software automatically calculates the radius
of rings and tabulates them. The picture along with the Table is printed by giving
print command as shown in Figure-10. The Table-1 is rewritten, as shown in Table-2,
for drawing the graph.
Table-1: Radius of various rings generated using sodium light
12. A graph is drawn taking (n+0.5) along the X-axis and (rn2 X10 -6) along the Y-axis, as
shown in Figure-11, and slope of the straight line is determined as
Slope = λR= 676x10 -9
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Figure-10: Different vertical lines shows the selection of different rings
Table-2: Ring numbers and diameters
૚
dn (µm)
rn (µm)
rn2 X10 -6
n+૛
n
rn2X10-6
1
2
3
4
5
6
7
8
9
10
11
12
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
1715.34
2336.84
2858.90
3293.95
3691.71
4052.18
4387.79
4710.97
4984.43
5257.89
5531.35
5817.24
857.67
1168.42
1429.45
1646.97
1845.85
2026.09
2193.89
2355.48
2492.21
2628.94
2765.67
2908.62
0.735
1.365
2.043
2.712
3.407
4.105
4.813
5.548
6.211
6.911
7.648
8.460
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
(n+0.5)
Figure-11: Variation of (n+0.5) with rn2
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13. With the wavelength of sodium yellow light as 589.3nm, one can calculate the radius
of curvature R.
Radius of curvature of the lens R = (676x10-9) / 589.3x10 -9 =1.14m
Part-B: Generation of Newton’s rings employing a solid state lamp and
determination of wavelength of LED light
In the first part of the experiment, we determine the radius of curvature of the lens used for
generating Newton’s rings using standard wavelength of sodium. In the second part we
determine unknown wavelengths of LED lights with known R.
14. The sodium vapour lamp is replaced by a solid state lamp and red LED light is
selected.
15. The rings are observed on the screen and their pictures are taken. The diameters of the
rings are obtained as discussed before and recorded Table-3.
16. The experiment is repeated for blue and green lights. In each case the radii of the
rings are calculated and presented in Table-3
Table-3: Radii of Newton’s rings employing LED lights of different colors and their
wavelengths
Color
n
n + 0.5 rn (µm) rn2 X10-6
Slope =λR X10-9
λ(nm)
1
1.5
609.07
0.370
713.66
626
Red
2
2.5 1019.26
1.030
3
3.5 1323.80
1.752
4
4.5 1584.82
2.511
1
1.5
522.06
0.2725
632.05
554
Green
2
2.5
950.90
0.9042
3
3.5 1243.00
1.5450
4
4.5 1472.96
2.1696
1
1.5
509.63
.2597
530.76
465
Blue
2
2.5
876.32
0.7679
3
3.5 1149.77
1.3219
4
4.5 1361.08
1.852
Results
The results obtained are tabulated in Table-4
Parameter
Radius of curvature (m)
Wavelength (nm)
Table-4: Experimental results
Light color
Red (LED)
Green (LED)
Blue (LED)
1.13
1.13
1.13
631
559
469
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Yellow (Sodium)
1.13
589.3
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Discussion
It has been a constant endeavour of the author to digitize physics lab instruments. A digital
eye-piece camera can be fitted with any optical instrument by removing the eye piece and
inserting the camera head in its place. The software provided can determine fringe width or
fringe radius, hence it can be used for many experiments in physics.
In the case of an LED, the total number of rings observed is less compared to that observed
using sodium light because sodium light is highly monochromatic whereas LED lights are
quasi-monochromatic. However, the average wavelength determined is reasonably accurate.
References
[1]
S P Basavaraju, Newton’s rings, Lab Experiments Vol-2, No-1, June-2002, Page-65
[2]
S P Basavarju, Wavelength and Energy gap determination using Newton’s rings
microscope in case of light emitting diodes, Lab Experiments Vol-2, No-2, Sept-2002,
Page-10
[3]
Jeethendra Kumar P K, Coherence length of a light emitting diode, Lab Experiments
Vol-10, No-3, Sept-2010, Page-215
[4]
Ajoy Ghatak, Optics, 3rd Edition, Tata-McGraw-Hill Publication, 2004, Page 13.18
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