Lab Experiments- KamalJeeth Instrumentation & Service Unit
Experiment-327
S
SODIUM DOUBLET WAVELENGTH
DIFFERENCE MEASUREMENTS
Dr D Sailaja and Dr K Chandrasekhara Reddy
Associate Professors, Department of Physics, S.S.B.N. Degree &P.G. College (Autonomous)
Anantapur-515001, AP, INDIA.
E-mail:[email protected]
Abstract
Fraunhofer diffraction has more important applications than the Fresnel type,
being the foundation of the theory of resolving power and of diffraction gratings.
Resolving power, given by λ/∆λ, is a measure of the capacity to separate the
images of two closely spaced objects where two lines of wavelengths λ and λ+∆λ
are just resolved or separated in the grating spectrum. Making use of this, the
wavelength difference between D1 and D2 lines of sodium is determined.
Introduction
The principle of rectilinear propagation is not strictly true, but only appears to hold if the
light is not restricted by small apertures. These deviations of light from rectilinear path are
called diffraction effects. They are characteristic of all kinds of wave motion. Thus it is a
common experience that water waves, sound waves, and radio waves bend around obstacles
so that no clear cut ‘shadows’ are observed. Light, on the other hand, seems to behave
differently. However, the small amount of diffraction is due to the wavelength of light being
small compared to the size of an obstacle or aperture commonly encountered. When the
magnitude of wavelength is not negligible compared to the size of an obstacle or aperture,
the same diffraction effects are observed as in the case of sound or other waves where similar
conditions hold.
Diffraction of light was discovered by Jesuit Father Francesco Grimaldi. Diffraction
phenomena are classified into two categories. When the waves are spherical, we have the
Fresnel diffraction phenomena and when the waves are plane, we have the Fraunhofer
diffraction phenomena.
Experimentally, the Fresnel diffraction phenomena are the simplest to observe, since there is
no requirement of lenses, but only a narrow source, diffracting aperture and screen are
required. However, the fact that the waves are spherical makes the mathematical theory more
complicated than that of the Fraunhofer diffraction phenomena which are observed when the
waves are plane. Fraunhofer diffraction has more important applications than the Fresnel
diffraction, being the foundation of the theory of resolving power and of diffraction gratings.
1
Vol-11, No-1, March-2011
Lab Experiments- KamalJeeth Instrumentation
I
& Service Unit
Theory
When a parallel beam of light of wavelength λ coming from an illuminated slit is incident
normally on a plane transmission diffraction grating placed with its lines parallel to the slit, as
shown in Figure-1,
1, the diffracted rays will appear at the focal plane of the telescope.
1: Palne wave incident on a diffraction grating
Figure-1:
If ‘θ’’ is the angle of diffraction of the nth primary maximum and ‘N’ is the number of lines
per centimeter ruled on the grating, then of lines per centimeter ruled on the grating, then
N=
λ=
Sinθ
nλ
Sinθ
nN
…1
…2
The number of lines per cm (N) of the grating surface can be determined from Equation
Equation-1,
knowing the wavelength ‘λ’’ and measured value of ‘θ’
‘ for a known order ‘n’.
If sodium light is used and D1 (589.6nm)
(589.6
and D2(589.0nm)) lines are resolved in the order ‘n’,
the wavelength ‘λ’ of the D2 line can be found from Equation-2,
Equation 2, from the known value of
‘N’ and measured value of ‘θ’.
Let the wavelengths of the D2 and D1 lines of sodium be λ and λ+∆λ respectively. The
resolving power of the grating is given by
λ
= nm
∆λ
…3
where ’n’ is the order number in which the D1 and D2 lines are just resolved by adjusting the
slit width , and ‘m’ is the total number of lines effective in the formation of the diffraction
pattern, i.e. the total number of lines exposed to the adjustable
ad
slit. If ‘x’ is the width of the
th
adjustable slit for which the n order fringe is just resolved, then m=Nx.
Equation-3 gives
λ
= nNx
∆λ
2
Lab Experiments- KamalJeeth Instrumentation
I
& Service Unit
Hence
∆λ =
λ
…4
nNx
Measuring ‘x’, the wavelength difference ‘‘∆λ’ can be found from Equation-4.
Equation
Apparatus used
Spectrometer, diffraction grating, mercury light, sodium light, adjustable slit
Procedure
a). Adjustment for normal incidence
Preliminary adjustments of the spectrometer are made and the slit of the collimator is
illuminated by sodium vapour lamp. The telescope is placed in line with the collimator. The
direct reading of the telescope is noted on both the verniers. Then the telescope is rotated
exactly through 90° and is fixed in this position.
The grating
rating is mounted on the prism table centrally with the ruled side of the grating away
from the collimator and the plane of the grating parallel to the line joining two of the leveling
screws L2 and L3 of the prism table as shown in Figure
Figure-2.
Figure-2
2: Grating mounted on prism table
The prism table is slowly rotated until the light from the collimator is reflected from the
unruled surface of the grating and forms the reflected image of the slit as observed through
the telescope. One of the screws L2 or L3 is adjusted so that the reflected image of the slit is
centrally situated in the field of view of the telescope. By this adjustment, the plane of the
grating is made to be vertical. The reading on the prism table is noted and then the prism
table is rotated exactly 45o such that the plane of the grating lies normal to the axis of the
collimator. The prism table is fixed in this position.
b). Determination of number of lines per cm length of the grating surface (N)
The telescope is released and brought in line with the collimator facing mercury vapour lamp.
lamp
When the telescope is moved on either side of the direct image, the diffracted images of the
first and the second order are observed.
3
Lab Experiments- KamalJeeth Instrumentation & Service Unit
The telescope is moved towards the right side of the direct image and focused for the first
order diffracted image of green line. The position of the telescope is adjusted until the vertical
crosswire coincides with the diffracted image of the green line. The reading of the telescope
on both the verniers is noted. Similarly the telescope is moved towards the left side of the
direct image and the vertical crosswire is made to coincide with the first order image of the
green line. Half of the difference between the two readings of the telescope gives the angle of
diffraction ‘θ’ for the first order spectrum.
The experiment is repeated for the second order spectrum and the angle of diffraction is
found. The readings are tabulated in Table-1 and number of lines per cm on the grating
surface is determined using the formula
N=
sin θ
nλ
10
The value of 1 main scale division, S =
= 30’
2
The number of divisions on the vernier scale, N=30
30'
S
=
Least Count (LC) of the spectrometer =
= 1'
N
30
Table-1
Order of the spectrum n =1
Color of the mercury spectral line Green
Reading of the telescope
VA
VB
V'A
V'B
65°09'
245°07'
26°35'
206°34'
2θ
VA~VB
V'A
~V'B
Average x
38°14'
38°13'
38°13'05″
Angle of
diffraction
࢞
θ=૛
19°06'32″
N=
ࡿ࢏࢔ࣂ
࢔ࣅ
5995
Determination of the number of lines per centimeter (N) on the surface of the grating
c) Measurement of wavelength of the D2 line
Table-2
Order of the spectrum n =1
Color of the mercury spectral line Sodium yellow (D2)
Angle of
Reading of the telescope
2θ
diffraction N=ࡿ࢏࢔ࣂ
࢞
࢔ࣅ
VA
VB
V'A
V'B
VA~VB V'A ~V'B Average x
θ=૛
65°59' 245°57' 24°38' 204°36' 41°22'
41°23' 40°41' 20°40'30″ 5889.4
To determine the wavelength λ of the D2 line
The Mercury light is replaced by sodium light and the D1 and D2 lines are observed. By
following the same procedure, the angle of diffraction for the D2 line is determined and
tabulated in Table-2. The wavelength of D2 line is determined by using the formula
λ=
sin θ
nN
4
Vol-11, No-1, March-2011
Lab Experiments- KamalJeeth Instrumentation & Service Unit
d). Measurement of the wavelength difference between D1and D2 lines of
the sodium light
An adjustable micrometer slit is mounted on the objective of the telescope. The least count
and the zero error, if any, of the micrometer screws are noted.
L.C of screw gauge = 0.01mm
Zero error =+10
Zero correction = -10
The telescope is now turned to the left to observe the resolved D1 and D2 lines of the first
order spectrum. The slit is first made wide and then slowly narrowed, so that the D1 and D2
lines of the first order in which they are resolved approach each other and just merge. At this
stage when the two lines are just resolved, the readings of the micrometer screw are noted.
The telescope is now turned towards the right and the above operations are repeated for the
lines of the same order. The mean of the readings ‘ x ’ (width of the slit) is calculated (Table3).
Table-3
Position
Order n
PSR(mm)
Left
Right
1
1
1
1
Coinciding Divisions
Observed
Corrected (n1)
Fraction
b=n1LC
(mm)
78
68
0.68
76
66
0.66
Determination of the width of the slit
Width of the slit
X=(a+b)mm
X in
(cm)
1.68
1.66
0.168
0.166
The average width of the slit x =0.167 cm.
The wavelength difference ‘∆λ’ between D1 and D2 lines of sodium is determined using the
formula
∆λ =
λ
nNx
=5.8825 x10-8 cm.
5
Vol-11, No-1, March-2011
Lab Experiments- KamalJeeth Instrumentation & Service Unit
Result and Conclusion
The number of lines per cm length on the grating surface N, the wavelength of the D2 line, λ,
and the wavelength difference between D1 and D2 lines of sodium are determined and
tabulated in Table-4.These are in good agreement with their corresponding standard values.
Table-4
Number of lines per cm
length on the grating
surface
‘N’
5995
Wavelength of the D2 line
‘λ’ A0
5889.4
Wavelength difference
between D1 and D2 lines of
sodium light
‘∆λ’ A0
5.8825
Experimental results
References
[1]
Joseph Valasec, Introduction to theoretical and experimental optics, John Wiley &
Sons Inc, New York.
[2]
2. H.C.Verma, Concepts of Physics, Vol-I, Bharathi Bhavan Publishers and
Distributors.
[3]
D.Chatopadhyay and P.C.Rakshit, An advanced course in Practical Physics, New
Ltd., Kolkata Central Book Agency (P) Ltd., Kolkata.
[4]
Samir Kumar Ghosh, A Text Book of Advanced Practical Physics, New Central Book
Agency.
6
Vol-11, No-1, March-2011